INTRODUCTORY MATHEMATICS AND STATISTICS 6TH EDITION SOLUTIONS MANUAL John S. Croucher Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd2 Solutions Manual, Chapter 4 Chapter 4 Ratios and proportions Quick Qui z 1.(c) 2.(d) 3.(b) 4.(d) 5.(a) 6.(c) 7.(c) 8.(d) 9.(a) 10. (b) Practice Questions 1.969102 100 =950 km per 100 litres 2.Number of bags =9 3.Current-asset ratio = $80 000=1.33 $60 000 This means that the business has $1.33 in current assets for every $1 in current liabilities. 4.Acid-test ratio =0.88 5.Debtor turnover =13.16 Average collection period = 36513.1627.74 days 6.Average stock =435 000 Stock turnover =2.87 Hence stock turns over 2.87 times per year or once every 127 days. 7.Yolande $36 000 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd3 Solutions Manual, Chapter 4 Susie $16 000 Bank $38 000 8.$600 000 9.24.1% 10. 43:70 Exercises 4.1(a) Percentage of 1L cartons sold =100 17%40 =42.5% Percentage of 600mL cartons sold =100 23%40 =57.5% (b) Number of 1L cartons sold =1740 6600 =2805 Number of 600 mL cartons sold =2340 6600 =3795 4.2(a) Percentage of 1L cartons sold =24% Percentage of 600 mL cartons sold =76% (b) Number of 1L cartons sold =0.24 6600 =1584 Number of 600 mL cartons sold =0.76 x 6600 =5016 4.3(a) 4 : 3(b) 1 : 6(c) 2 : 5 4.4(a) 13 : 8(b) 3 : 4(c) 3 : 4 4.5Petrol usage =1650125 km/L =13.20 km/L =1320 km/100 L 4.613 200 metres/L 4.7(a) J anuary118.2 February100.0 March61.1 April25.1 (b) J anuary 18.2% increase March April 38.9% decrease 74.9% decrease Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd4 Solutions Manual, Chapter 4 4.8 (a) J anuary 470.6 February398.0 March243.1 April100.0 (b) J anuary 370.6% more February298.0% more March143.1% more 4.9(a) 56822 25.82 pairs/minute (b) 56822 60 1549 pairs/hour (c) 22 60568 1 pair every 2.32 s 4.10Sandra $13 750, Don $22 000, Annette $19 250 4.11Sandra =$165 000 0.12 =$19 800 Don =$165 000 0.56 =$92 400 Annette =$165 000 0.32 =$52 800 4.12Total asset turnover =$385 000 2.533 $152 000 4.13Current-asset ratio =$132 000 1.10 $120 000 This indicates that the company has $1.10 in assets for every $1 in current liabilities owed. 4.14Current-asset ratio =$52 000 =0.80 $65 000 This indicates that the bookstore has 80 cents in current assets for every $1 in current liabilities owed. 4.15Acid-test ratio =$132 000 $48 000 =1.12 $120 000 $45 000 4.16Acid-test ratio =$52 000 $14 000 =0.86 $65 000 $21 000 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd5 Solutions Manual, Chapter 4 4.17This means that in the previous year the local council had 67 cents in current assets for every $1 in current liabilities owed, while this year the figure had dropped to 58 cents. 4.18(a)Thismeansthatinthepreviousyearthislocalcouncilhad76centsincurrent assets for every $1 in current liabilities owed, while this year the figure increased to $1.77. (b) Possibly the neighbouring council since the figure of $1.77 indicates it could readily meet its obligations. 4.19(a) Debtor turnover =$1 550 000 =8.807 $176 000 (b) Average collection period =365 days =41.44 days 8.807 4.20Carmel $600, J ack $1000, Mick $650, Tanya $250 4.21Current-asset ratio =43 000 =1.65 26 000 This indicates that the company has $1.65 in current assets for every $1 in current liabilities owed. 4.22Total asset turnover =250 000 =2.58 97 000 2.58 100 =258% This indicates that there was a 258% turnover in sales in relation to assets; or for every $1 of total assets the company generated sales of $2.58. 4.23(a) Total asset turnover =237.5% (b) For every $1 of total assets, the company can generate sales of $2.38. 4.24(a) Average stock =$110 000 +$230 000 =$170 000 2 Stock turnover ratio =$625 000 =3.676 $170 000 On average, the stock turns over 3.68 times per year or onceevery 3653.68 =99 days. Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd6 Solutions Manual, Chapter 4 4.25(a) Average stock =$730 000 Stock turnover =$ 1 320 000 1.808 $ 730 000 (b) Stock turns over about every 202 days. 4.26Bank overdrafts are not usually included in the calculation of the quick-test ratio since it is uncommon for banks to demand sudden repayment of such overdrafts. 4.27The quality of assets is an indication of how readily such assets can be converted into cash to meet company obligations. 4.28Check methods and answers are reasonable. 4.29(a) Donna $31 666.67, Michael $9333.33, Annie $34 000 (b) Donna $40 000, Michael $16 000, Annie $44 000 (c) Donna $60 000, Michael $32 000, Annie $68 000 4.30From Exercise 4.29 (a) Michael =$9333.33(b) Michael =$16 000(c) Michael =$32 000 If Michael is paid a straight salary of $25 000, under profits (a) and (b) Michael is better off under the new arrangement. 4.31Vijays average monthly investment =$444.44 =21% Irenes average monthlyinvestment =$1666.67 =79% (a) Vijay =$4 200, Irene =$15 800(b) Vijay =$8 400, Irene =$31 600(c) Vijay =$21 000, Irene =$79 000 4.32(a) Peter =0.35 (50 000) =$17 500 Alan =0.35 (50 000 17 500) =$11 375 David =50 000 17 500 11 375 =$21 125 (b) Peter =$20 000 Alan =0.35 (100 000 20 000) =$28 000 David =100 000 20 000 28 000 =$52 000 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd7 Solutions Manual, Chapter 4 4.33(a) Equal share =$16 666.67 Peter =$833.33, worse off Alan =$5 291.67, better off David =$4 458.33, worse off (b) Equal share =$33 333.33 Peter =$13,333.33, better off Alan =$5,333.33, better off David =$18,666.67, worse off 4.34Goals 20, behinds 45 4.3512 goals scored, 20 behinds scored 4.36(a) Average =(4 15) +(6 24) =20.4 10 (b) Average =(8 15) +(12 24) =20.4 20 4.37Browsing =100 customers; Buying =60 customers 4.38There are 0.50 160 =80 male customers Of these, 0.60 80 =48 males who browse, and 0.40 80 =32 males who buy Therefore 52 females browse and 28 females buy. The female ratio is 52:28 or 13:7. 4.39Let length of block A =L metres Let width of block B =W metres Data: (120 +2W) (60 +2L) =40 or 2W 2L = 20 (1) also, 3060 =58 or 4L = 5W(2) Solving (1) and (2) yields W =40 and L =50 Therefore area of block A =30 50 =1500m2 Area of block B =40 60 =2400 m2 4.40Let radius of circle X =x metresLet radius of circle Y =y metresData: 2x +2y =70(1)

2

2 =169

or 9x2 =16y2 (2) Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd8 Solutions Manual, Chapter 4 Substitute for y in (2) using (1): 9x2=16(35 x)2 7x2 1120x +19600 =0 x2 160x+2800 =0 (x 20)(x 140) =0 x =20 or 140 Ruleout140sinceitisunfeasible. ThereforeradiusofcircleX= 20m Radius of circle Y =15m. 4.41Number in age group under 15 years =49 004 031 28.5% =13 966 149 Number in age group 1664 =49 004 031 65.8% =32 244 652 Number in age group 65 years and over=49 004 031 5.7% =2 793 230 4.42Total asset turnover =$7.43 million =2.902 $2.56 million 4.43(a) Debtor turnover=$2.73 million=3.33 $0.820 million (b) Average collection period =365days =110 days 3.33 4.44Current-asset ratio =$734 542 =1.542 $476 241 This indicates that the company has $1.54 in assets for every $1 in current liabilities owed. 4.45Acid-test ratio=$734 542 $382 345 =2.63 $476 241 $342 168 Since this is more than 100%, this would not be of concern. 4.46Daily rate of sales = 83 +43=126 =2.8 22 +23 45 4.47Petrol usage =84 =7.24 km/L 11.6 =724 km/100 L Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd9 Solutions Manual, Chapter 4 4.48Speed of the ship =1460 =7.60 km/h 8 24 4.49 1 gallon1mile =4.54609188 litres1.609344 kilometres =2.8248litreskilometre

1 gallon28 miles=4.54609188 litres1.609344 kilometres 28=2.8248 litres per kilometre28= 0.1009litreskilometre

28 miles per gallon is equivalent to 10.09 litres per 100 kilometres 4.50 62472 100 =866.67 km per 100 litres 4.51No. of 5kg bags sold =32 58 =20 4.52$1 250 000 =1.61 $776 200 This means that the business has $1.61 in current assets for every $1 in current liabilities. 4.53Debtor ratio =$876 750 =11.82 $74 200 Average collection period =36511.82 =31 days 4.548:15 4.5539:32 4.56Total asset turnover = $2 300 000=185% $1 240 000 4.57Stock turnover =$536 000($860 000 $786 000)/2 + =0.65 4.58Total asset turnover = $475 200=0.54 $887 300 4.59 4+124 6 8 12 + + + =1630 4.60 0.543.60 =15%