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Bô.#-@ ™}@#(Ãïòòåãô¡þ. 6ƒ.¸"@6ƒ./¸@6ƒ.s/'6œ-@ ¹"'6¢-@/¹! š}6¢-@&/N-@@ !¹"D(Your time was: ¸ SecondƒN B!+/ 6….0/¹!@6 ›}….s; :/F-@@ F(Your time was: ¹ Minute…¸ SecondƒD/ 6š-š%¹N/ 6›-›%¸v/$þSC-F:A0,% œ}AV$F:A1,F:A2,%AV$F:A3,O@1S ÿ3F:A8,%AV$F:A9,%@@D2:PRO }GMC€ B'fŽèŽ©R©©7  Sä0à©€ Sä0Ö ¹Ù€ðˆõ`Lwä &h»€A„T @€;@@,@6€.) 26-@Ÿ}d,,@@ D2:CTRLFILEn @p6-@s‚-@x @€(@ }‚ ‚Œ@È,,@@ D2:CTRLFILEÉ6-@ @Í6-@ Ò;.(@¡}Fractions, Decimals, Percents;(@Ü1$(@Exponents and Roots1(@æ x > 1, which of the following›T›could not be x?›1›8/6›2›5/4›3›15/11›4›10/7›5›12/9›E›7/5 = 1.40, thereý}fore 1.40 > x > 1 ›E› ›E›Change fractions to decimals:›E› 8/6 = 1.33, 5/4 = 1.25, 15/1þ}1 = 1.36›E›10/7 = 1.43,12/9 = 1.33 ›E›Only 1.43 is greater than 1.40.›››››››››››››››››››0015›C›282›T›One fifth of one hour ÿ}equals what›T›fraction of a week?›1›168›2›1/168›3›1/840›4›1/960›5›It cannot be determined from the ›5› information given}.›E›1/5 of one hour * 1/24 (hours in a ›E›day) * 1/7 (days in a week) ›E› ›E›1/}5 * 1/24 * 1/7 = x›E› 1/840 = x›››››››››››››››››››0016›E›347›T›If 10% of x = 75, then 250% of x =›1›250›2›500›3›750}›4›1,500›5›1,875›E›Do the problem in two steps: ›E›1. Change 10% to a fraction: 1/10›E› Then: 1/10x = 75›E› } x = 750›E›2. Change 250% to a fraction: 2 1/2›E› Then: 2 1/2 * 750 =›E› 5/2 * 750 = 1,875 ›E›NOTE: Y}ou could use decimals instead›E›of fractions to solve this problem.›››››››››››››››0017›D›396›T›In each of the following pairs} of ›T›fractions and percents, which pair is›T›not equal in value?›1›3/8 = 37 1/2%›2›3/9 = 33 1/3%›3›7/8 = 87 1/2%›4›4/9 }= 42 2/3%›5›5/8 = 62 1/2%›E›Change both the fractions and percents›E›to decimals:›E› ›E›3/8 }= .375, as does 37 1/2%;›E›3/9 = .333, as does 33 1/3%;›E›7/8 = .875, as does 87 1/2%;›E›4/9 = .444, NOT .427;›E›5/8 = .625, }as does 62 1/2%.›››››››››››››0018›B›346›T›If A percent of B is C, then AB/C =›1›1›2›100›3›C›4›B›5›A›E›Plug numbers into the p }roblem: If 10›E›percent of 50 is 5, then 10 * 50/5 = ›E›100. ›E› ›E›NOTE: This method will work fo }r any›E›numbers as long as you keep the per-›E›cent correct in the first half of the›E›problem. For example, 20 percent of 50 }›E›is 10, or 25 percent of 20 is 5.›››››››››››››››0019›B›248›T›A bank account containing $5,000 is›T›increased by one percent }. What is›T›the account balance after the ›T›increase?›1›$5,005›2›$5,050›3›$5,500›4›$5,055›5›$5,550›E›First calculate } one percent of $5,000:›E›(1% = .01) .01 * $5,000 = $50›E›Then add: $5,000 + $50 = $5,050›››››››››››››››››››››0020›D›372›T›If} a yacht with a list price of ›T›$11,450 is discounted 15%, how much›T›money would a buyer pay for the yacht?›1›$10,450}›2›$9,875›3›$9,750›4›$9,732.50›5›$9,676.50›E›First find out the amount of the dis-›E›count: (15% = .15)›E›$11,450 * .15 = }$1,717.50 ›E› ›E›Then subtract: $11,450.00›E› -1,717.50›E› ----------›E› } $ 9,732.50››››››››››››››]/12›2›7/6›3›71/60›4›37/30›5›83/60›E›Find the lowest common denominator. In›E›this case, it#›0021›B›191›T› 2 ›T›(x - 36)/(x - 6) =›1›x - 6 ›2›x + 6 ›2› 2 ›3›x + 6 ›4›x - 1›5›x + 1›E› } 2 ›E›First factor:(x - 36) = (x - 6)(x + 6)›E›Then divide: (x - 6)(x + 6)/(x - 6) =›E› x + 6›››››››››››››››››}››››0022›E›355›T› 4 3 2 2 ›T›(18x - 15x + 9x ) / 3x =›1›6x - 5x + 3›1› 3 ›2›6x + 5x + 3 ›2› } 2 ›3›6x + 5x - 3›3› 2 ›4›6x - 5x - 3›4› 2 ›5›6x - 5x + 3 ›E› 2 ›E›Divide ea}ch term by 3x separately: ›E› ›E› 4 2 3 2 2 2 ›E› 18x /3x - 15x /3x + 9x /3x = ›E› } 2 ›E› 6x - 5x + 3›››››››››0023›C›280›T› 5 3 2 4 ›T›(-7a b ) (-8a b ) = ›1›-15ab›1› 10 12 ›2›-56}a b ›2› 7 7 ›3›56a b ›3› 7 7 ›4›-5a b ›4› 10 12 ›5›56a b ›E›Multiply coefficients and add e}xpo- ›E›nents of the same base: ›E› ›E› 5 3 2 4 7 7›E› (-7a b ) (-8a b ) = 56a b ›››››}››››››››0024›D›165›T›Factor: 3xy + 6xz + 9x ›1›x(3y + 6z + 9)›2›y(3x + 6z + 9)›3›3x(y + 2z + 3x)›4›3x(y + 2z + 3) ›5›3x(3y +} 6z + 9)›E›Factor out 3x from each term of the›E›polynomial: 3x(y + 2z + 3).›››››››››››››››››››››››››››››0025›E›203›T›If -15}s + 12 + 20s + (-9) = -2, ›T›then s = ›1›5›2›-5›3›0›4›1›5›-1›E›-15s + 12 + 20s + (-9) = -2 ›E› -15s + 20}s = -2 - 12 + 9 ›E› 5s = -5 ›E› s = -1 ›››››››››››››››››››››››0026›D›288›T›If 3x =} 9 and 3y = 12, then 5xy =›1›5›2›12›3›45›4›60›5›540›E›Complete the problem in steps: ›E› ›E› 1. Solve for x: 3x} = 9›E› x = 3 ›E› 2. Solve for y: 3y = 12 ›E› y = 4›E› 3. Substitute:  } 5xy = 5 * 4 * 3›E› 5xy = 60 ›››››››››››››››››0027›A›127›T›3(a + 2b) + (-1) (b + 2a) =›1›a + 5b›2›a + 7b!}›3›5a + 7b›4›-a - 5b ›5›5a + 5b›E›3(a + 2b) + (-1) (b + 2a) =›E› 3a + 6b + (-b) + (-2a) = a + 5b›››››››››››››››››››››››››››"}››0028›C›251›T›If 4 * 5 * 6 = a and 4 * 6 = b, then›T›a + b is equal to the product of 12 ›T›and›1›6›2›10›3›12›4›16›5›20›E›#}Do the problem in steps: ›E› ›E› a = 4 * 5 * 6 = 120›E› b = 4 * 6 = 24›E› a + b = 24 + 120 = 144›E› $} 12x = 144›E› x = 12›››››››››››››››0032›C›256›T›If 3x + 4y = 8 and 2x + 3y = 4, then ›T›5x +%} 5y =›1›12›2›16›3›20›4›24›5›30›E›Do the problem in two steps: ›E› ›E› 1. 3x + 4y = 8 ›E› -(2x + 3y =&} 4)›E› ------------ ›E› x + y = 4 ›E› ›E› 2. 5(x + y) = 5 * 4 = 20 ›'}››››››››››››››0033›B›345›T›The by-laws of a particular club state›T›that no member can be on more than two›T›committees. If t(}here are 45 members in›T›the club, what is the greatest number ›T›of 15-member committees the club can›T›have at one time?›1›)}15›2›6›3›5›4›4›5›3›E›If each member serves on two commit- ›E›tees, there are 90 membership places›E›on the committees. 90/15*} = 6 fifteen-›E›member committees.›››››››››››››››0034›C›354›T›If Mr. Grunska bought a dinner and›T›drink for $7.50 and the di+}nner cost›T›four times as much as the drink, how›T›much did the drink cost? ›1›$1.00›2›$1.25›3›$1.50›4›$2.00›5›It cannot be d,}etermined from the ›5› information given›E›Let x = the cost of the drink and›E› 4x = the cost of the dinner ›E› ›E›-} x + 4x = 7.50 ›E› 5x = 7.50 ›E› x = 1.50 ›››››››››››››0035›B›178›T›If twice an intege.}r is 15 more than ›T›-3, then that integer is ›1›9›2›6›3›3›4›-6›5›-9›E›Let x = the integer: 2x = -3(+15)›E› /} 2x = 12›E› x = 6›››››››››››››››››››››››››0036›E›296›T›If Ms. Wallace earns 8% simple inter- ›T›est 0}per year on a $7,500 investment, ›T›how much will she earn over a three-›T›year period? ›1›$600›2›$900›3›$1,200›4›$1,500›5›$11},800›E›First find out the interest for one›E›year: .08 * $7,500 = $600 per year›E› ›E›Then multiply by 3: 3* 600 = $1,8002}›E›over three years ›››››››››››››››››0038›B›253›T›If Gayle is now three times as old as›T›she was eight years ago, how old is3}›T›she now? ›1›8 ›2›12›3›16›4›24›5›32›E›Let x = Gayle's present age and (x-8)›E›= her previous age: x = 3(x - 8)›E› 4} x = 3x - 24›E› 24 = 2x ›E› 12 = x ›››››››››››››››››››0039›B›490›T›If two ai5}rplanes take off from St. ›T›Louis at the same time and fly in›T›opposite directions at 550 miles per›T›hour and 650 miles6} per hour, respec-›T›tively, how many hours after take-off›T›will they be 5,100 miles apart? ›1›3 1/2 ›2›4 1/4 ›3›4 3/4 ›4›5 7}›5›5 1/4 ›E›Let x = number of hours›E›The distance traveled by first plane›E›plus the distance traveled by second›E›plane equ8}als the distance they are›E›apart. ›E› ›E›Set up an equation and solve:›E›(550 mi./hr.* x) + (650 mi./hr.* x) =›E›5,100 mi9}. ›E›1,200x = 5,100›E›x = 4.25 = 4 1/4 ›0040›D›417›T›If a rectangle with an area of 10›T›square inches has a width 3 inches›T:}›less than the length, what is the›T›length in inches? ›1›2›2›3›3›4›4›5›5›6›E›Let x = length and x - 3 = width:›E› ;}l * w = a ›E› (x) (x-3) = 10›E› 2 ›E› x - 3x = 10 ›E› 2›E› x - 3x - 10 = 0›E›Factor: (x-5) <}(x+2) = 0›E›Either x - 5 = 0 and x = 5 or›E› x + 2 = 0 and x = -2›E›x cannot be a negative number.›E›Therefore, x must =}be 5.›E›Check: 5(5-3) = 10 ›0029›D›341›T›If Megan weighs eight times as much›T›as her newborn sister and if their›T›combined>} weight is 54 pounds, what›T›is Megan's weight in pounds?›1›8›2›42›3›45›4›48›5›51›E›Let x = the newborn sister's weight›E›and?} 8x = Megan's weight›E› ›E›Solve for x: x + 8x = 54 ›E› 9x = 54 ›E› @} x = 6 ›E›Megan's weight = 8x = 8 (6) = 48 ›››››››››››››0030›D›194›T›If xyz = 0, txz = 1, and tys = 0, ›T›which of tA}he following must be 0? ›1›none ›2›t›3›x›4›y›5›z ›E›If txz = 1, then none of these terms›E›equals 0. ›E›If xyz = 0 and x B}and z do not equal ›E›0, then y must be 0. ›››››››››››››››››››››››0031›D›367›T›A painter has painted all but one of›T›four eqC}ual sized walls of a storage›T›building. If he has already used 12x›T›gallons of paint, how much paint will›T›he need for theD} final wall?›1›x›2›2x›3›3x›4›4x›5›6x›E›Let y = entire job›E› ›E›Set up the equation: ›E›3/4 = 12x/y ›E› 3y = 48x ›E› y =E} 16x gallons needed for the job›E›16x - 12x = 4x gallons needed for the›E› final wall ›››››››››0037›C›350›T›TF}he sum of which three consecutive ›T›even integers is closest to but not›T›greater than 85? ›1›18, 20, 22›2›22, 24, 26›3G}›26, 28, 30 ›4›30, 32, 34 ›5›34, 36, 38 ›E›Let x, x + 2, and x + 4 represent the›E›integers: x + (x+2) + (x+4) < 85›E› H} 3x + 6 < 85›E› 3x < 79›E› x < 26.33›E› I} x = 26››››››››››››››››››] ›T›(x - 36)/(x - 6) =›1›x - 6 ›2›x + 6 ›2› 2 ›3›x + 6 ›4›x - 1›5›x + 1›E›  1ï?A„W€A€@ B'` SAT›1 +A!K}1AAR@-@@((         --@@ 2(      !L}  7-@@<(        A-@@F(           K-@@P(       !M}  U-@@Z(        _-@@a(           n€-@A €È +!N}Ê'AR@'AÍ'@‚'@ƒ@9Ò--@@-(COPYRIGHT (C) 1984 æ!O}<-@@<("by Harcourt Brace Jovanovich, Inc.ð.-@@.(All rights reserved.ú-@@!P}''(No copy of the computer program:-@@:( embodied in this diskette may be4-@@4(ma!Q}de without prior written"8-@@8(permission from the publisher.,)-@@ )(VERSION 1.1A ATõ!R}%D:PROGMø2 #B'd!ƒ-AVAg%"‚+ƒ‚/ ƒ2#ùN„;@,"6„. h©   \ä`B6„7@<@,.>:Ab!S},N6-?:C:„,,ü00165,16,41,127,133,16,141,14,210,108,96,228›ý$þSC€-F:A0,%AV$F:A1,F:A2,%AV$!T}F:A3,O€@1S €ÿ3F:A8,%AV$F:A9,%@@D2:HELLOC€ B'f+A k›0001›D›108›T›(5x + 2y) + (2x - 3y) =›1›3x - y›2›3x + 5y›3›7x + y›4›7x - y›5›7x - 5y›E› 5x + 2y ›E›+ 2x - 3y ›E›--------%V}- ›E› 7x - y ›››››››››››››››››››››››››0002›B›337›T› 3 2 ›T›(15x - 20x + 5x) / 5x = ›1›3x - 4 ›%W}1› 2 ›2›3x - 4x + 1 ›2› 2 ›3›5x + 4x ›3› 2 ›4›5x + 4x - 1 ›4› 2 ›5›x + 4 ›E›Divide ea%X}ch term of the polynomial›E›by 5x separately: ›E› ›E› 3 2 ›E› (15x - 20x + 5x%Y}) / 5x = ›E› 2 ›E› 3x - 4x + 1›››››››››0003›E›168›T›If x + 6 = 11, then x - 5 = ›1›12›2›10›3›8›4›5›5›0›E%Z}›Do the problem in two steps: ›E› ›E›1. Solve for x: x + 6 = 11›E› x = 5›E› ›E›2. Subtr%[}act: 5 - 5 = 0›››››››››››››››››››››0004›E›280›T› 2 3 2 ›T›(-4x y) (3x y ) = ›1›-12xy ›1› 5 2 ›2›12x y%\} ›2› 6 2 ›3›-12x y ›3› 5 3 ›4›12x y ›4› 5 3 ›5›-12x y ›E›Remember to multiply coefficients›%]}E›and add exponents of the same base: ›E› ›E› 2 3 2 5 3›E› (-4x y) (3x y ) = -12x y ›››%^}››››››››››0005›C›364›T›(x + 5) (x + 6) = ›1›2x + 11x + 11 ›1› 2 ›2›x + x - 30 ›2› 2 ›3›x + 11x + 30 ›3› %_} 2 ›4›x - 11x - 30 ›4› 2 ›5›x + x + 30›E›Use the foil (first, outer, inner, ›E›last) method to multiply the %`} ›E›equations: ›E› ›E› 2 ›E›(x + 5) (x + 6) = x + 6x + 5x + 30›E› %a} 2 ›E› = x + 11x + 30 ›››››››››0006›B›232›T› 2 ›T›If a = 1/3, then a + 2a = ›1%b}›2/3›2›7/9›3›8/9›4›5/6›5›17/18›E›Substitute 1/3 for a: ›E› ›E› 2 2 ›E› a + 2a = (1/3) + 2 * 1/3 %c}= ›E› 1/9 + 2/3 = ›E› 1/9 + 6/9 = 7/9 ›››››››››››››››››››0007›D›283›T› 5 3 2 %d}2 ›T›84 X Y / -7X Y =›1›11XY›1› 3 2 ›2›-11X Y ›2› 3 ›3›12X Y ›3› 3 ›4›-12X Y›4› 7 5 ›5›-12%e}X Y ›E›Remember to divide the coefficients ›E›and subtract the exponents of the ›E›same base: ›E› ›E› %f} 5 3 2 2 3 ›E› 84X Y / -7X Y = -12X Y›››››››››››0008›B›205›T›If the sum of twice an integer and›T›21 %g}is 83, what is that integer? ›1›28 ›2›31›3›33›4›37›5›41›E›Set up an equation and solve: ›E› ›E› 2x + 21 = 8%q}ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ3 ›E› 2x = 62 ›E› x = 31 ›››››››››››››››››››››0009›B›257›T› 2 ›T›If x - 7x + 12 is grea%r}ter than ›T› 2 ›T›x + 7x + 12, then which of the ›T›following must be true of x? ›1›x > 0 ›2›x < 0 ›3›x = 0›4›x = 3%s} ›5›x = 4 ›E›The two equations are identical except›E›for -7x and 7x. If -7x > 7x, then x›E›must be a negative number x < 0. %t}›››››››››››››››››››0010›C›254›T›If the Bears' score of 39 points was›T›one less than twice the Cowboys'›T›score, what was the%u} Cowboys' score?›1›18›2›19›3›20›4›21›5›22 ›E›Let x = Cowboys' score ›E› ›E›Set up the equation and solve: ›E› %v} 2x - 1 = 39 ›E› 2x = 40 ›E› x = 20 ›››››››››››››››››0011›E›287›T› 2 3 3 2 ›T›(ab%w} c ) (a b c) = ›1›4a4b4c ›1› 4 4 3 ›2›a b c ›2› 3 2 3 ›3›a b c ›3› 4 2 4 ›4›a b c ›4› 4 4 4 ›5›a b %x}c ›E›To multiply powers of the same base,›E›simply add the exponents: ›E› ›E› 2 3 3 2 4 4 4 %y} ›E› (ab c ) (a b c) = a b c ›››››››››››››0012›D›239›T›If twelve-year-old Katie is one fourth›T›as old as her father,%z} how old is her›T›father? ›1›36›2›40›3›44›4›48›5›52›E›Let x = age of Katie's father›E› ›E›Set up an equation and solve: ›%{}E› 12 = 1/4x ›E› (4)12 = (4)1/4x ›E› 48 = x ›››››››››››››››››0013›D›363›T›If the sum of x and y is%|} 8 and the›T›difference is 14, what are x and y? ›1›8 and 14 ›2›1 and 3 ›3›5 and 3 ›4›11 and -3 ›5›5 and -3 ›E› %}} ›E› ›E› x + y = 8 ›E› + x - y = 14 ›E› ------------ ›E› 2x = 22%~} ›E› x = 11 ›E› ›E›Solve for y: x + y = 8›E› 11 + y = 8 ›E› y = -3 ›››››%}››››0014›C›377›T›When 5 + 4x is subtracted from the sum›T› 2 2 ›T›of 5 - x and 2x + 5x + 1, what is ›T›th%€}e difference?›1›2x + x + 1›1› 2 ›2›x + 9x + 11 ›2› 2 ›3›x + x + 1›3› 2 ›4›3x + x + 1›4› 2 ›5›3x + 9x%} + 1›E› 2 2 ›E›Add: (2x + 5x + 1) + (-x + 5) = ›E› 2 ›E›(x + 5x + 6) ›E› 2 %‚} ›E›Subtract: (x + 5x + 6) - (4x + 5) =›E› 2 ›E›(x + x + 1)›››0015›B›310›T›If (4x - 3) (x + 2) = ›T›(2x - 1) (%ƒ}2x + 1), then x = ›1›0›2›1›3›3›4›4›5›6›E›Use the foil method: ›E› ›E› (4x - 3) (x + 2) = (2x - 1) (2x + 1)›E› 2 %„} 2 ›E› 4x + 8x - 3x - 6 = 4x + 2x - 2x - 1 ›E› 2 2 ›E› 4x + 5x - 6 = 4x - 1 ›E› %…} 5x = 5 ›E› x = 1 ›››››››››››››0016›C›241›T›If 5x - 4 = 31 and x + y = 5, then y =›1›-5›2›-4›%†}3›-2›4›0›5›2›E›Do the problem in two steps: ›E› ›E› 1. Solve for x: 5x - 4 = 31›E› 5x = 35›E› %‡} x = 7 ›E› ›E› 2. Solve for y: 7 + y = 5›E› y = -2›››››››››››››››››0017›B›%ˆ}283›T›If the perimeter of a rectangle is 8›T›feet and its area is 3 square feet, ›T›what is its length in feet? ›1›2›2›3›3›4%‰}›4›5›5›6›E›If the rectangle's area is 3 square›E›feet, the width is likely to be 1 foot›E›and its length 3 feet. Check the pe%Š}r-›E›imeter: (perimeter) = 2(b * h) ›E›1+1+3+3=8›››››››››››››››››››0018›C›358›T›If 3a + 3b + ab + 9 = 0 and if›T›a + 2%‹} = 6, then b + 2 = ›1›-9›2›-3›3›-1›4›0›5›3›E›Do the problem in steps: ›E› ›E›1. Solve for a: a + 2 = 6›E› %Œ} a = 4 ›E› ›E›2. Substitute:(3*4) + 3b + 4b + 9= 0›E› 12 + 3b + 4b = -9 %}›E› 7b = -21›E› b = -3 ›E› ›E›3. b + 2 = -3 + 2 = -1›››››››››%Ž}0019›B›493›T›If the sum of the squares of two con-›T›secutive odd integers is 202, what are›T›those integers?›1›7 and 9›2›9 a%}nd 11›3›11 and 13›4›13 and 15›5›15 and 17›E› 2 2 ›E›a + b = 202. Remember that the ›E%}›numbers are consecutive odd integers,›E›then ›E› ›E› 2 2 ›E›Estimate: 10 + 10 = 200, ›E%‘}› 2 2›E›then 9 + 11 = ›E› 81 + 121 = 202 ›E› ›E›If you are confused by estimating, ›E›plug%’} answers into the equation and ›E›eliminate incorrect answers.›0020›D›154›T›If a(4b) = (5) (16), then ab - 2 =›1›24›2›22›3›%“}20›4›18›5›16›E› a(4b) = 80›E› a(4b)/4 = 80/4›E› ab = 20›E› ab - 2 = 18›››››››››››%”}›››››››››››››››]x + 2y) + (2x - 3y) =›1›3x - y›2›3x + 5y›3›7x + y›4›7x - y›5›7x - 5y›E› 5x + 2y ›E›+ 2x - 3y ›E›--------$›0001›A›121›T›If 3x + 7 = -26, then x =›1›-11›2›-15›3›-19›4›-26›5›-33 ›E›Solve for x: 3x + 7 = -26›E›Subtract 7: 3x = -3)–}3›E›Divide by 3: x = -11›››››››››››››››››››››››››››0002›D›156›T›If 3x + 5 = 4x - 3, then x =›1›1›2›-2›3›2›4›8›5›-8›E›Sol)—}ve for x: 3x + 5 = 4x - 3›E›Add 3 to each side: 3x + 8 = 4x›E›Subtract 3x from ›E› each side: 8 = x›››)˜}››››››››››››››››››››››0003›E›213›T›If 7x + 5 = 8x + 10, then x =›1›1›2›-1›3›3›4›5›5›-5›E›HINT: Be careful with the signs of›E)™}›the numbers. ›E› 7x + 5 = 8x + 10›E›Subtract 5: 7x = 8x + 5›E›Subtract 7x: 0 = x + 5 ›E›S)š}ubtract 5: -5 = x ›››››››››››››››››››››0004›B›177›T›If a + 4 = a - b, then b =›1›4›2›-4›3›2a + 4›4›2a - 4›5›-2a - 4›E)›}› a + 4 = a - b ›E›Subtract a from ›E› both sides: 4 = -b›E›Reverse the signs: )œ} -4 = b›››››››››››››››››››››››››0005›A›176›T›If x = 9 and y = 5, then›T›(x/3 - y/5) / (xy/9) =›1›2/5›2›5/2›3›17/45›4›9/2›5›)}2/9›E›Substitute the values of x and y in›E›the equation and solve: ›E› ›E›(9/3 - 5/5) / (9 * 5/9) = ›E› ›E›(3 - 1)/5 = )ž}2/5 ›››››››››››››››››››0006›C›247›T›If a = 3x and b = 2/(9x + 5), what is›T›b in terms of a?›1›1/(4a + 3)›2›1/(4.5a + 2.5)›3›)Ÿ}2/(3a + 5)›4›2/(9a + 5)›5›2/(9a + 15)›E›Solve for x: a = 3x therefore x = a/3 ›E›Then solve for 9x: 9x = 9a/3 = 3a ›E›Now sub) }stitute in the equation: ›E›b = 2/(3a + 5) ›››››››››››››››››››››››0007›A›348›T›Suppose x is an integer. How many ›T›integ)¡}ers are both less than x and ›T›greater than x - 1? ›1›0›2›1›3›2›4›3›5›It cannot be determined from the›5› information pro)¢}vided ›E›Remember that integers are whole num-›E›bers. Therefore, there are none be-›E›tween x and x - 1. Substitute an›E›in)£}teger for x: There are no integers›E›between 5 and 5 - 1, for example. ›››››››››››››››››0008›E›266›T› )¤} 2›T›If x - 2 = 9, then (x + 2) =›1›63›2›81›3›121›4›144›5›169›E›Do the problem in two steps:›E›Solve for x: x - 2 = )¥}9 ›E› x = 11 ›E› ›E› ›E›Substitute value 2 2›E› for x:)¦} (11 + 2) = 13 = 169›››››››››››››››››0009›A›228›T›If 15 + a + b = 37 and if a + b = c,›T›then 25 - c = ›1›3›2›9›3›15›4›)§}22›5›47›E›Substitute c for a + b: ›E› ›E› 15 + c = 37 ›E› c = 37 - 15›E› )¨} c = 22; then ›E› 25 - c = 25 - 22 = 3›››››››››››››››››››0010›E›272›T›If (a - 5) (3/a) = 0 and a does not›T›equal)©} 0, then a =›1›3/5›2›-3/5›3›-3›4›3›5›5›E›In order for the equation to equal›E›zero, one of the multiplied terms›E›must equal )ª}zero. If a does not = 0,›E›then (a - 5) = 0 or 3/a = 0. If a›E›does not = 0, then 3/a cannot be zero.›E›Therefore, a - 5 = 0 )«}and a = 5.›››››››››››››››››››0011›A›205›T›a/3 + (b + c)/3 = ›1›(a + b + c)/3 ›2›(a + b + c)/6 ›3›(a + b + c)/9 ›4›a + b + c›)¬}5›a + (b + c) ›E›Remember that when adding fractions›E›with the same denominator, you retain›E›the common denominator and add)­} the›E›numerators. ›››››››››››››››››››››››››0012›D›230›T›Under which of the following condi- ›T›tions must y - x equal a po)®}sitive ›T›number? ›1›y < 0›2›x < 0›3›x = y›4›x < y›5›x > y›E›If you are looking for a positive›E›number, set up the equation )¯}y - x > 0.›E›If y - x > 0, then y > x or x < y.›››››››››››››››››››››››0013›E›376›T›If x is greater than zero, which of ›T›t)°}he following is greatest?›1›x ›1› 2 ›2›x ›3›x/2 ›4›1/x ›5›There is insufficient information to›5› determine the answ)±}er ›E› 2 ›E›If x is an integer, x is the ›E›greatest. But x may be a fraction, ›E› )²} 2›E›in which case x becomes smaller. In›E›order to solve the problem you must ›E›know if x is an integer or a fraction.›)³}››››››››››››0014›B›154›T›If 7x - 8 = 7y + 6, then x - y = ›1›-2›2›2›3›-6›4›-14›5›14 ›E›Solve for x - y:›E› 7x - 8 = 7y + 6›)´}E› 7x - 7y = 6 + 8 ›E› 7(x - y) = 14; divide both sides by 7›E› x - y = 2 ›››››››››››››››››››››››0015›C›447›T›If a and b)µ} are positive integers, and›T›if a - b = 9, what is the least possi-›T› 2 ›T›ble value of (a + b) ?›1›81)¶}›2›100›3›121›4›144›5›169›E›In order to find the least value for›E›a + b, substitute the least possible›E›values for a - b. Re)·}member the least›E›possible value for the smaller of the›E›two (b) is 1, since a and b are posi-›E›tive integers. ›E› )¸} ›E› 10 - 1 = 9›E› ›E› 2 ›E› (10 + 1) = 121›››››0016›B)¹}›417›T›Two is less than or equal to A.›T›A is less than B. B is less than›T›or equal to 7. A and B are integers.›T›What is th)º}e least possible value of›T›(A + B)/AB?›1›9/14›2›13/42›3›14/49›4›2/7›5›5/14›E›In order to find the least value of›E›a fractio)»}n (A + B)/AB, make the›E›denominator as large as possible. ›E› ›E›If 2 is less than or equal to A, A is›E›less than B. B )¼}is less than or equal›E›to 7. Then 6 + 7/6 * 7 is the smallest›E›fraction. 6 + 7/6 * 7 = 13/42.›››››››››0017›D›216›T›If x = 5)½}/2 and y = 2/3, then›T›(x + y) - (xy) = ›1›2/3›2›5/6›3›4/3›4›3/2›5›9/5›E›Substitute for x and y and solve: ›E› ›E› (5)¾}/2 + 2/3) - (5/2 * 2/3) =›E› (15/6 + 4/6) - (10/6) = ›E› (19/6) - (10/6) = 9/6 = 3/2›››››››››››››››››››››0018›A›1)¿}99›T›If the sum of r - 1, r - 2, and›T›r - 3 = 0, then r = ›1›2›2›-2›3›0›4›1›5›-1›E›Solve for r:›E›(r - 1) + (r - 2) + (r - 3)À}) = 0›E› 3r - 6 = 0›E› 3r = 6›E› r = 2››››››››››››››››››)Á}›››0019›C›410›T›If a is greater than zero, which of›T›the following must be true? ›T› ›T›I. a/a = a ›T›II. a/1 )Â}= 1›T›III. a/a = 1 ›1›I only ›2›II only ›3›III only ›4›I and III ›5›II and III ›E›In order to check the values, substi-›E)Ã}›tute values in the equations:›E› ›E›I. 2/2 cannot equal 2. ›E› (1/2) / (1/2) cannot equal 1/2.›E›II. 2/1 can)Ä}not equal 1. ›E› (1/2) / 1 cannot equal 1. ›E›III. 2/2 equals 1.›E› (1/2) / (1/2) equals 1. ›››››0020›E›306›T›If 1)Å}7 + xy = 18 + 17, then the pair›T›x,y could be any of the following›T›except ›1›18,1›2›9, 2›3›2, 9›4›6, 3›5›9, 3›E›Do the )Æ}problem in two steps:›E› ›E› 17 + xy = 18 + 17 ›E› xy = 18 ›E› ›E›If xy = 18,)Ç} then the possible pairs›E›are (18, 1), (9, 2) and (6, 3). Only ›E›(9, 3) could not be x, y.››››››››››››››]ct 7: 3x = -3(k›0001›B›177›T›.007 is the ratio of 7 to ›1›100›2›1,000›3›10,000›4›1/1,000›5›1/10,000›5› ›E›Change the decimal to a frac-É}tion:›E›.007 = 7/1,000 ›E›The denominator is the›E›other term in the ratio. ›››››››››››››››››››››››0002›E›106›T›What is the r-Ê}atio of .75 to 3/4? ›1›1:4›2›4:1›3›3:4›4›4:3›5›1:1›E›Because .75 = 3/4, their ratio is 1:1.›››››››››››››››››››››››››››››››000-Ë}3›C›140›T›What is the ratio of 8 inches to 1 ›T›yard? ›1›1:4›2›2:3 ›3›2:9›4›1:6›5›1:8›E›Change the yard into inches and s-Ì}et›E›up the ratio as a fraction: ›E›8/36 = 2/9 ›››››››››››››››››››››››››0004›E›332›T›If 3 out of every 7 seniors in a class›T-Í}›of 350 intend to graduate early, how›T›many seniors intend to graduate early?›1›3›2›50›3›70›4›140›5›150›E›Let x = number of -Î}graduates ›E›Now set up a ratio (be sure that›E›3 corresponds to x and 7 corresponds›E›to the total number of seniors): ›E› -Ï} ›E› 3/7 = x/350›E› 7x = 1,050›E› x = 150 ›››››››››››››0005›A›200›T›In a certain clas-Ð}s, the ratio of›T›juniors to seniors is 4 to 1. What›T›percent of the class is seniors? ›1›20›2›25›3›50›4›75›5›80›E›If the ra-Ñ}tio is 4:1, then 4/5 are›E›juniors and 1/5 are seniors. 1/5 = 20%›››››››››››››››››››››››››0006›D›266›T›Which of the following-Ò} cannot be the›T›ratio of three sides of a triangle?›1›3:3:3›2›3:3:5›3›3:4:5›4›3:4:7›5›3:6:8›E›Remember that the sum of two s-Ó}ides of ›E›a triangle must be greater than the ›E›third side. In the ratio 3:4:7, two›E›sides would be equal to the greatest›-Ô}E›side.›››››››››››››››››››››0007›D›418›T›A $42,000 estate was to be divided›T›among three heirs in a ratio of›T›1:2:4. What w-Õ}as the amount of the›T›largest inheritance? ›1›$6,000›2›$12,000›3›$18,000›4›$24,000›5›$30,000 ›E›The largest share has a rati-Ö}o of 4 to›E›7 to the entire estate (4 of the 7 ›E›shares). ›E›Let x = amount of largest inheritance›E› ›E›Set up the rati-×}o:›E› 4(shares) / 7(total shares) = ›E› x/42,000 (total amount) ›E›4/7 = x/42,000 ›E›7x = 168,000 ›E› x = 24,000››››-Ø}›0008›E›121›T›If 3x + 3y = 0, then the ratio of›T›x to y is›1›3:1›2›1:3›3›-1:3›4›1:1›5›1:-1›E›If 3x + 3y = 0, then 3x = -3y a-Ù}nd ›E›x = -y. ›››››››››››››››››››››››››››0009›B›267›T›Patrick is one year older than›T›Stephen, who is three times as old›T›a-Ú}s Mary. If Patrick is 37, how old›T›is Mary? ›1›10›2›12›3›18›4›21›5›36›E›Let x = Mary's age; 3x = Stephen's ›E›age; 3x + 1-Û} = Patrick's age›E› ›E›Set up the equation:›E› 37 = 3x + 1›E› 36 = 3x ›E› 12 = x ›››››››››››››0-Ü}010›C›387›T›If two boys divide their $23.10 ›T›newspaper route earnings in the›T›ratio of 3:4, what is the smaller›T›share? ›-Ý}1›$3.30›2›$6.60›3›$9.90›4›$11.55›5›$13.20 ›E›The ratio of the smaller share to the›E›entire sum is 3:7 (3 of the 7 shares).›E-Þ}›Let x = amount of the smaller share ›E› ›E›Set up the ratio: ›E› 3(shares) / 7(total shares) = ›E› x/23.10 (tota-ß}l earnings)›E› 3/7 = x/23.10 ›E› 7x = 69.30 ›E› x = 9.90 ›››››››0011›D›309›T›If four painters who work at the-à} same›T›rate can together finish painting a›T›house in six days, what part of the›T›whole job can one painter do in a›T›day? -á}›1›1/4 ›2›1/6›3›1/12›4›1/24›5›1/36›E›One painter is 1/4 of the crew. One›E›day is 1/6 of the time. One painter›E›can do 1/4 o-â}f 1/6 of the job in a day.›E›1/4 * 1/6 = 1/24 ›››››››››››››››››0012›C›223›T›If the weight of 21 yards of rope is›T›6 pounds, -ã}what is the weight in pounds›T›of 49 yards of rope? ›1›10›2›12›3›14›4›15›5›16›E›Let x = weight of larger rope ›E› ›E›Set u-ä}p the ratio:›E›21 yards/49 yards = 6 pounds/x›E›21/49 = 6/x›E› 21x = 294›E› x = 14›››››››››››››››0013›E›441›T›A certain c-å}hemical is to be diluted›T›with water so that the ratio of the›T›chemical to water will be 1/9. If ›T›two three-liter contain-æ}ers of the›T›chemical are used, how many liters of›T›water are necessary to obtain the›T›correct ratio? ›1›9›2›18›3›27›4›45›5-ç}›54›E›There are 6 liters (two three-liter›E›containers) of the chemical.›E›Let x = amount of water needed ›E› ›E›Set up t-è}he ratio:›E›1(part chemical)/9 (parts water) = ›E›6(liters chemical)/x (liters water) ›E›1/9 = 6/x ›E› 54 = x ›››0014›B›233›T-é}›If the ratio of x to y is 2 to 3 and›T›the ratio of y to z is 1 to 4, what›T›is the ratio of x to z? ›1›1:12 ›2›1:6 ›3›1:4 ›-ê}4›1:3›5›2:5›E› x/y = 2/3 and y/z = 1/4›E› x/y * y/z = x/z›E›Therefore, 2/3 * 1/4 = 2/12 = 1/6››››››-ë}›››››››››››››››››0015›C›503›T›A 24-foot-long log is sawed into three›T›sections. If the first section is 2›T›feet longer than-ì} the second and the ›T›second is 2 feet longer than the ›T›third, what is the ratio of the third›T›section to the whole -í}log? ›1›1/8›2›1/6›3›1/4›4›1/3›5›2/5›E›Let x = third section, x + 2 = second›E›section, x + 4 = first section ›E› ›E›Set up-î} the equation:›E› x + (x + 2) + (x + 4) = 24 ›E› 3x + 6 = 24›E› 3-ï}x = 18›E› x = 6›E›The ratio is 6/24 = 1/4.›››››0016›B›386›T›If at a certain time of day, a verti--ð} ›T›cal yardstick casts a 27 inch shadow, ›T›what is the length in feet of the ›T›shadow of a 42 foot telephone pole?›1›30›2›-ñ}31.5›3›33›4›34.5›5›36›E›Let x = length of shadow of 42 foot›E›pole ›E›Set up the ratio:›E›27 inches/ 36 inches = x feet/ 42 f-ò}eet›E› ›E› 3/4 = x/42›E› 4x = 126›E› x = 31.-ó}5 ›››››››››››0017›C›468›T›On a scale drawing where 6 inches›T›represents 12 1/2 feet, how many›T›inches represent 150 feet? ›-ô}T› ›1›50›2›60›3›72›4›90›5›120›E›1. Convert in. to ft.: 6 in. =›E› 1/2 ft. ›E›2. Find out how many feet 1 foot rep-›E-õ}› resents: 1/2 ft. = 12 1/2 ft.›E› 1 ft. = 25 ft.›E›3. Let x = number of feet that repre-›E› s-ö}ents 150 feet ›E› Set up ratio:›E› 1 ft./25 ft. = x/150 ft.›E› 25x = 150 ›E› -÷} x = 6 ›E›Change back to inches: 6 ft. = 72 in. ›››0019›E›202›T›If x and y vary proportionately and if›T›x is 3 when y is 15-ø}, what is y when›T›x is 20? ›1›40›2›50›3›75›4›80›5›100›E›Set up the ratio: 3/15 = 20/x›E› 3x = 300 ›E› -ù} x = 100›››››››››››››››››››››››0020›C›424›T›If a rectangle and a triangle have the›T›same base and same he-ú}ight, what is the›T›ratio of the area of the rectangle to›T›the area of the triangle?›T› ›1›1:1›2›1:2›3›2:1›4›1:3›5›It cannot-û} be determined from the›5› information given ›E›Remember that the area of a rectangle ›E›= b * h and the area of a triangle-ü} =›E›1/2 b * h. If the rectangle and the›E›triangle have the same base and ›E›height, the area of the rectangle is›E›tw-ý}ice the area of the triangle. ›››››››››››0018›B›268›T›Five radios cost as much as two tape ›T›players. If tape players cost $-þ}45 ›T›each, what is the cost of each radio? ›1›$15›2›$18›3›$24›4›$27›5›$30›E›If one tape player costs $45, then two›E›tap-ÿ}e players cost $90, and five radios›E›also cost $90. One radio costs 1/5 of ›E›$90. 1/5 * $90 = $18 ››››››››››››››››››››››]ac,{