Fundamentals Of Business Mathematics In Canada, First Canadian Edition Solution Manual

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1Review and Applications ofBasic MathematicsExercise 1.148820824201.21836261218.320428162832824.4183621892224.520428208820.61836266224.75436425494492.6631643998393358222.954364218618360 522..83512365123953933510222.6848216642448113322.4416844244812232.255453009510033510320175463132222.512810012410434212234234142222..99819214020937582015.000501005811951625195165195162222222,.$100.740.007397261$1000.061$1001736545.$194.171.03$2000.031$2000.091$20018.12451.453$1025.1500$05.1500$05.01500$.192221.1061$1.0612081000$02.11000$02.011000$.203300.204$04.00816.0100$04.0104.1100$04.0104.01100$.2122

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Exercise 1.1(continued)04.574$03.0942596.01300$03.00609.111300$03.003.0111300$.222Concept Questions (Section 1.2)1.You must retain at least one more figure than you require in the answer. To achieve four-figure accuracy in the answer, you must retain a minimum offive figuresin the valuesused in the calculations.B)2.We want six-figure accuracy in the answer. Therefore, values used in the calculationsmust be accurate to at leastseven figures.B)3.We want seven-figure accuracy in the answer. Therefore, values used in the calculationsmustretainat leasteight figures.C)4.To be accurate to the nearest 0.01%, an interest rate greater than 10% must have four-figure accuracy. Therefore,five figuresmust be retained in numbers used in thecalculations.C)Exercise 1.2%500.8787500.0.187%500.6262500.0.210465%00.2353500.2.32047%25.565625.0.4169%00.1404000.1.52535%00.1282800.11.6257%5000.2025000.0.7100025%0.4000000.40.8251000%00.2020200.22.91002%38.1343438.11.103211%000.7575000.0.11505.37%50.1878750.1.12125.22130 8383 356... %Exercise 1.2(continued)142 6266 683...%  1577 7777 779... %1611 09109 09111...%

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1711111 1109... %180 0040 44900... %  %...592225900192707201 370137 0373727...%381138451121...64696455922...554505545454023...100049100024..00210023456125...030410030405026...1040095154027...00909100090909028...%...667161666702961%...67116166713067310 01666716667160...%3222 5556255 5659...%330 6849368 493250365...%%...1096404109603436515350 00916670 916670 1112...%.%....7916700079167036120950$94.681.02915$920.0951$9237365112.$104.581.04583$1000.111$10038.125$410.990.903750$454.760.1051$454.76391211.$711.981.110767$790.840.131$790.8440365311.$3384.521.031164$34900.1251$34904136591.Exercise 1.2(continued)$10,524.800.95013699$10,0000.101$10,000.42365182$720.041.0525$6501$65043.2220.105

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$906.130.97625$950.751$950.75.442240.095$14,435.881.0108333$15,4001$15,40045.66120.13$439.791.05750$5501$55046.4420.11547. =0.x $1527 =$509.0048. 0.0275 x $2.75 =$0.0849. 2.50 x $25 =$62.5050.0.00025 x $200 =$0.0551. 0.5 x $30 =$15.0052.Money available to be spent on entertainment is 100–(53+42) = 5%In dollars, 0.05 x $14,775 =$738.75They can spend $738.75 on entertainment.53. Sales of in-store products = 0.36 x $102,300 = $36,828HST collected on in-store products = 0.13 x $36,828 =$4,787.6454.Shots scored from 2-point zone = 0.54545433 = 18Shots scored from 3-point distance = 0.4666715 = 7Foul shots scored = 0.79329 = 23Total points scored = 18(2) + 7(3) + 23(1) =80$6648.461.0280821.035630$66000.12510.0851$660055.36582365153$893.381.068641.22398$78011$780.568120.10520.0825$7159.480.00750.05369613$100011$100057.120.097120.09$1708.140.03965320.008125$350111$35058.5120.0975120.0975$1830.07$950011$950059.0.018750.0973321640.075540.075

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$1011.38$848.75$162.64$848.750.041850.151251$451.178205$10000.041851$451$1000111$4560.1.1782051420.083720.0837420.083761. Seats not sold to season-ticket holders = 100%–67.5% =32.5%Number of seats not sold to season-ticket holders = 0.325 x 19289 = 6,269 seatsRounded to the nearest 100,6300seats were not sold to season-ticket holders.62.Percentage of impurities = 100%99.95% = 0.05%Amount of impurities = 0.000531.16 g = 0.01558 g =15.58 mg63.Portion of commission retained = 0.604.8% = 2.88%Income is 2.88% of sales =0.0288 x $5,225,000 =$150,480That is, $150,480 = 0.0288SalesStan’s commission was$150,480.64.If 18% of $128,500 is lower than $23,820 then that will be the contribution.0.18 x128,500=$23,130Maximum RRSP contribution is$23,130since it is lower than $23,820.

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Exercise 1.31.Regularweekly earnings =52$58,800= $1130.77Equivalent hourly rate =35$1130.77= $32.31Overtime hourly rate = 1.5($32.31) = $48.47Gross pay for 39-hour week = $1130.77 + 4($48.47) =$1324.652Regular biweekly earnings =26$37,500= $1442.31Equivalent hourly rate =37.52$1442.31= $19.23Gross earnings = $1442.31 + 9(1.5)$19.23 =$1701.923.Regular biweekly earnings =26$54,600= $2100.00Equivalent hourly wage =402$2100.00= $26.25Hasad worked 3 hours of overtime in the first week and 6.5 hours in the second week.Gross pay = $2100.00 + 9.5(1.5)$26.25 =$2474.064.Annual earnings = 52(40)$31.50= $65,520Equivalent semimonthly earnings =24$65,520=$2730.005.Regular hours worked = 7.5 + 7.5 + 6 + 6 + 7.5 = 34.5Overtime hours worked = 4.5 +1 + 1.5 =7Gross earnings = 34.5($17.70) + 7(1.5)($17.70) =$796.50

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Exercise 1.3(continued)6.Total hours worked = 51.5 of which 8 hours were worked on a statutoryholiday.Overtime hours worked = 51.5–(40 + 8) = 3.5Regular earnings = 40($34.50)= $1380.00Overtime pay= 3.5(1.5)$34.50=$181.13Holiday pay= 8($34.50)=$276.00Holiday premium = 8(2)$34.50=$552.00Gross earnings=$2389.137.Output in excess of quota = 4 + 6 + 7 + 8 +10 =35 shirtsTotal pay = 40($7.50) + 35($3.00) =$405.008.Weight packed per day = 7.5(250)(0.500kg) = 937.5 kg.Earnings per day = 7.5($8.25) + (937.5–500)($0.18) =$140.639.October earnings = (# renewals)$20 + (# new policies)$35 + 0.055(Total premiums)= 126($20) + 37($35) + 0.055($14,375 + $47,880)=$7239.0310.Annual sales = 12($11,000) = $132,000Hillary’s earnings = 0.21($132,000) + 0.07($132,000–$100,000) =$29,96011.Estimated earnings from Supreme Audio &Video = $2000 + 0.04($55,000) =$4200Estimated earnings from Buy-Right = $1500 + 0.03($25,000) + 0.06($55,000–$25,000)=$405012.a.Earnings will be the greater of$600 or 0.11(Sales) = 0.11($5636) =$619.96b.The salesman will earn the $600 from sales if0.11(Sales) = $600That is, ifSales =110600.$=$5454.55per week13.Gross earnings = 0.033($50,000) + 0.044($50,000) + 0.055 ($40,000)=$6050.0014.a.Earnings = $2000 + 0.022($227,000–$150,000) =$3694.00b.Average earnings = $2000 + 0.022($235,000–$150,000) =$3870.00For a straight commission rate to generate the samemonthly earnings,Commission rate =1.6468%100%$235,000$387015.a.Earnings = 0.05($20,000) + 0.075($20,000) + 0.10($14,880) =$3988.00b.For the same earnings from a single straight commission rate,Commission rate$54,880 = $3988.00Commission rate =$54,880$3988100% =7.267%16.Commission earned = $630.38–$300 = $330.38Hence,0.03(Sales subject to commission) = $330.38Sales subject to commission =0.03$330.38= $11,012.67Total sales = $11,012.67 + $20,000 =$31,012.67

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Exercise 1.3(continued)17.Commission earned in August = $3296.97–$1500.00 = $1796.97Hence,Commission rate ($151,342–$100,000) = $51,342Commission rate =$51,342$1796.97100% =3.50%18.Commissionearned on first $90,000 of sales was0.04($40,000) + 0.05($50,000) = $4100Commission earned on sales in excess of $90,000 was $5350–$4100 = $1250That is,0.06(Sales exceeding $90,000) = $1250Sales exceeding $90,000 =0.06$1250= $20,833.33Total sales for the month = $90,000 + $20,833.33 =$110,833.3319.Required monthly commission = $4000–$2000 = $2000Commission income on first $50,000 of monthly sales is0.03($50,000–$25,000) = $750The combinedcommission and bonus rate on sales exceeding $50,000 is 3% + 3% = 6%.Hence,0.06(Sales exceeding $50,000) = $2000–$750Sales exceeding $50,000 =0.06$1250= $20,833.33Required monthly sales =$70,833.33Concept Questions (Section 1.4)1.You should calculate a weighted averagewhen some of the values being averaged aremore important or occur more frequently than other values.2.The weighted average will equal the simple average when the items being averaged allhave the same weighting factor. This will happenwhen each of the values beingaveraged has the same importance, or occurs the same number of times.3.If youinvest the same amount of money in each investment, each rate of return has thesame importance. The portfolio’s rate of return will then equal the simple average of theindividual rates of return.

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Exercise 1.41.Weight each number of TV sets per household by the number of homes with that numberof TVs. The weighted average number of TVs per household in the survey sample is2540)(51)(1402)(833)(224)(4=1.53Based on the survey, we estimate the average number of TVs per household to be 1.53.2.The weighted average cost per share is1800$21.75300$19.00500$15.631000=$17.593We should weight each "goals against" figure by the number of games in which thatnumber was scored.GAA =1 02 13 24 37 42 61 1020=3.504.The amount of sales subject to each commission rate should be used as the weightingfactor.a.The average commission rate will be$60,0006%$10,0004%$20,0003%$30,000=3.83%b.The average commission rate will be:$100,0006%$50,0004%20,0003%$30,000=4.70%5.The weighted average interest rate that willbe charged on the new $57,500 balance is()()50057700020850037,,+,$%$%$=7.65%6.The weighted grade point average isGPA =5 2 33 2 74 3 32 173 3 04 2 0534234......=53 221.=2.537.Weight each score by the number of students who obtained that score. The weightedaverage score is2 106 99 87 73 62 51 330=7.538.Weight each semester's GPA by the number of credits on which the respective GPA wasobtained. The cumulative GPA is6 3 59 3 012 2 757 5 3 269127 5......=105 034 5..=3.049.Note that the age of receivables (rather than the dollar amount of receivables) is to beaveraged. The relative importance of each of the three age classifications is determinedby the dollar amount in each category. Hence, the weighting factors are the respectivedollar amounts of receivables. The (weighted) average age of accounts receivable is$20,745$907,350$1325$6850$12,57090$132560$685030$12,570=43.74 daysExercise 1.4(continued)

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10.The rate of return for the entire portfolio is the weighted average return on the fivesecurities in the portfolio. Each rate of return should be weighted by the fraction of themoney invested in the respective security. The rate of return on the portfolio is1.0027%0.2012%0.3513%0.1010%0.2014%0.15=12.40%11.a.The weighted average cost of units purchased during the year is1800$10.97500$10.471000$10.86300=$10.67b.The weighted average cost of the beginning inventory and units purchased during theyear is1956$10.6741800$10.55156=$10.66c.Value of ending inventory = 239Weighted average cost= 239($10.66)=$2547.7412.The weighted average price increase was1.0015%0.505%0.2010%0.30=9.50%13.Each “Menu price as a % of cost” should be weighted by the fraction of revenue obtained from the respect25.015.050.010.0%25025.0%22515.0%20050.0%30010.0=226.25%of input costsOn average,Menu prices = 2.2625(Input costs)Therefore, Input costs =2625.2pricesMenu= 0.44199(Menu prices)On average, input costs are44.20%of revenue.14.PeriodBalanceNo. of days1st to 7th$35,00078th to 24th$35,000 + $10,000 = $45,0001725th to 31st$45,000–$20,000 = $25,0007The weighted average balance on the loan was7177$25,0007$45,00017$35,0007=$38,225.81MenucategoryMenu price(as % of cost)% of totalrevenueAppetizers30010Entrees20050Desserts22515Beverage25025

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Exercise 1.4(continued)15.We want the average number of peopleworking over the course of the year.Thegivenfiguresforthenumberofemployees added or laid off at varioustimesareusedtodeterminethecumulativenumberofpeopleemployed.Each number in the third columnmustbeweightedby thenumberofmonths in the second column. The average number employed was12203341403291211143=25.5016.Thegivenfiguresfortheamountinvested from time to time are used todetermine thecumulativeinvestmentThe (weighted) average investment was12$1000574632761993721571=$71,333.3317.Eachnumberofsharesinthethird column must be weightedby thenumber of months in thesecond column. The (weighted)averagenumberofsharesoutstanding was  12million125725656352..= 6.25 million =6,250,00018.a.Each cost in the third column mustbe weighted by the amount of theingredientintheDeluxeNutCombo.The(weighted)averagecost is3.04.05.0125)40.6($3.0)60.3($4.075.2$5.050.11$150.9$295.2$5=$5.433/kgLien’s average cost is$0.543per 100 gb.The retail price is 1.50($0.543) =$0.81per 100g.PeriodNo. ofmonthsNumber ofemployeesJan. 1 to Mar. 31314Apr. 1 to Apr. 30114 + 7 = 21May 1 to May 31121 + 8 = 29June I to Aug. 31329 + 11 = 40Sept. 1 to Sept. 30140–6 = 34Oct. 1 to Dec. 31334–14 = 20No. ofCumulativePeriodmonthsinvestmentSept. 1 to Sept. 301$57,000Oct. 1 to Oct. 31172,000Nov. 1 to Jan. 31399,000Feb. 1 to Feb. 28176,000Mar. Ito Apr. 30263,000May 1 to Aug. 31457,000No. ofNumber of sharesPeriodmonthsoutstanding (millions)Jan. 1 to Feb. 2825Mar. 1 to May 3135 + 1 = 6June 1 to Oct. 3156 + 0.5 = 6.5Nov. 1 to Dec. 3126.5 + 0.75 = 7.25WeightIngredient(kg)Cost per KgPeanuts5$2.95Cashews2$9.50Almonds1$11.50Sunflowerseeds0.5$2.75Raisins0.4$3.60Smarties0.3$6.40

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Exercise 1.51.QuarterSales–PurchasesGST Remittance(Refund)1$155,365$7768.252(340,305)(17,015.25)3408,64820,432.404164,8188240.902.HST RemittanceMonthSales–Purchases(Refund)March$(77,760)$(10,108.80)April(8255)(1073.15)May136,51517,746.95June114,87514,933.753.The GST charged in each case will be0.05($39,500) = $1975.00a.With no PST in Alberta, the totalamount paidwill be$39,500 + $1975.00 =$41,475.00b.PST inSaskatchewan= 0.05($39,500) = $1975.00Totalamount= $39,500 + $1975.00 + $1975.00 =$43,450.00c.PST in Quebec = 0.09975($39,500) = $3940.13Totalamount= $39,500 + $1975.00 + $3940.13=$45,415.134.Cost inManitoba=$1000 + GST + PST = $1000 + 0.05($1000) + 0.08($1000) = $1130.00Cost inPEI= $1000+HST = $1000 +0.14($1000)= $1000 + $140= $1140.00The consumer will pay$1140.00–$1130.00 =$10.00more inPEI.5.a.The HSTreported fora $39.45(pre-tax) item is0.13($39.45) =$5.13.b.The HST inclusive price is $39.45 + $5.13 = $44.58. If $50 cash is paid, change will bebased on the rounded price of $44.60. Therefore, change will be $50-$44.60 =$5.40.6.TheHST rate inNew Brunswickis13%.For each $100 of pre-tax price, the tax-inclusive price must includeHST of $13. That is,atax-inclusive price is $113includes$13ofHST.The HST is, therefore,100%×$113$13=11.50% of the HST-inclusive priceConsequently, a$495 tax-inclusive price includesHST =0.1150×$495=$56.937.Property tax =$3827.88$227,000100016.8629=valueAssessed1000rateMill8.a.0.1 mill = $0.10 per $1000 of assessed value =$0.01 per $100of assessed valueb.Property tax increase =0 11000.$200,000 =$20.00

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Exercise 1.5(continued)9.Total taxes =$467,00010004.6423$143,000100015.0294= $2149.204 + $2167.954=$4317.1610.a.Current year’s taxes =$298,000$100$1.52193$4535.35Previous year's taxes =$285,000$100$1.56324$4455.23Change in property taxes =$80.12increaseb.For the current year’s taxes to remain at $4455.23,$100ratetaxNew$298,000 = $4455.23New tax rate =$100$298,000$4455.23$1.49504 per $100of assessed value11.a.Tax increase =Mill rate increase1000Assessed value$2,430,000 =Mill rate increase1000$6,780,000,000Mill rate increase =1000$6,780,000$2430= 0.3584Next year’s mill rate = 7.1253 + 0.3584 =7.4837b.Next year's assessment = 1.05($6.78 billion) =$7.119 billionNext year’s budget = Current year's taxes + $2,430,000=100012537.$6.78billion+ $2,430,000=$50,739,534Next year’s school mill rate applied to next year’s assessment must generateenough tax revenue to meet next year’s budget. That is,$50,739,500 =billion$7.1191000ratemillNewNew mill rate =7.1273$7,119,0000$50,739,5012.Current budget = Last year’s budget + $750,000=$750,000+billion$1.563$100$0.94181=$15,470,490.3Current assessment = $1563 million + $97 million = $1660 millionHence,$15,470,490 =$100ratetaxNew$1660 millionNew tax rate =$0.93196$1,660,000$1000$15,470,49That is, the tax rate would have to be$0.93196 per $100of assessed value.

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Review Problems1.a.8220382220322323= 25–2010 = 25–2 =23b.45410232232= 4(29–8)2÷(10–20)= 4102÷(–10)=–40c.$213.8510 095512.= $213.85(1–0.039583) =$205.39d.365770.08251$2315=1.0174041$2315=$2275.40e.$325.7510 10542.$325.75(1.053189) =$343.08f.1.145266$7101$710320.0925=$619.94g.$885.75365490.07751$476.503652310.07751= $885.75(1.049048)–1.010404$476.50= $929.194–$471.593=$457.60h.$859320.0825120.0825$6821121= $859(1.020767) +1.013797$682= $876.839 + $672.718= $1549.562.a.96–(6–42) x 7–2 = 96–(–10)7–2 =164b.81÷(52–16)–4 (23–13) = 81÷9–4(–5) =29c.365410.1251$531.490.1251$827.69365273=1.093493$827.69$531.49(1.014041)= $756.923 + $538.953=$1295.88d.$550.45365990.08751$376.293651950.08751= $550.45(1.046747)–1.023733$376.29=$208.62e.$11373120.097521$2643120.09751= $1137(1.016316) +1.024574$2643=$3735.163.0.62 x 99 =$61.38Review Problems(continued)

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4.0.80 x$156.25 =$125.005.0.0075 x$ 133.=$1.006.Two hours = 2(60) = 120 minutes0.125 x 120=15minutes7.Actualprofit =0.90 x $23,400 =$21,060.008.Price increase = 0.35×$2.20 = $0.77Selling price = $2.20 + $0.77 =$2.97per share9.a.Gross biweekly earnings =26$56,600= $2176.92Equivalent hourly wage =37.52$2176.92=$29.03b.Total remuneration= $2176.92 + 4.5(1.5)$29.03 =$2372.8710.Gross biweekly earnings =26$61,000$2346.15Equivalent hourly rate =75$2346.15$31.28Gross pay = $2346.15 + 33(1.5)$31.28 =$3894.5111.Total hours worked = 41 hoursOvertime hours worked = 1.5 (on Wednesday)+ 0.5 (on Friday) = 2 hoursRegular hours worked = 41–2 (hrs of overtime)–3 (hrs on stat holiday) = 36 hoursRegular earnings = 36($42.50)= $1530.00Overtime pay= 2(1.5)$42.50=$127.50Holiday pay= 7.5($42.50)=$318.75Holiday premium = 3(2)$42.50=$255.00Gross earnings=$2231.2512.Gross earnings = $1000 + 0.08($10,000) + 0.10($38,670–$30,000) =$266713.Commission earnings = Commission rate (Sales–$40,000)$3188.35–$1000 = Commission rate ($88,630–$40,000)Commission rate =$48,630$2188.35100% =4.50%

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