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 2 Chapter 2 Percentages Quick Quiz 1.(c) 2.(d) 3.(a) 4.(d) 5.(d) 6.(a) 7.(c) 8.(a) 9.(b) 10. (b) Practice Questions 1.74.8% 2.$3846.15 3.17.5% 4.Land tax payable =$100 +0.016($ 875 000 $ 396 000) =$7764 5.$325 6.$1200.60 7.$504.90 8.20% 9.$ 47.80 10. Income tax payable =$17 547 +($180 000 $115 200) 45% =$46 707 Medicare levy payable =0.015 $115 200 =$1728 Total personal tax payable =$48 435 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd3 Solutions Manual, Chapter 2 Exercises 2.1(a) 25%(b) 3313 c) 12.5% 2.2(a) 41.67%(b) 37.50%(c) 75% 2.3(a) 72%(b) 50.5%(c) 82.73% 2.4(a) 940(b) 23 (c) 78 2.5(a) 0.7(b) 0.3072(c) 0.16 2.6(a) $625(b) $3150(c) $7250 2.7(a) $650(b) $2450(c) $3875 2.8(a) If total sales prices are less than $20 000, then prefer Exercise 2.7. If total sales prices are more than $20 000, then prefer Exercise 2.6. (b) What sales prices you expect to have. (c) Prefer Exercise 2.7 where commission =$425 (Using Exercise 2.6, commission =$375.) 2.9(a) 1%(b) 0.75%(c) 3.25% 2.10Total brokerage payable =$75 +($2500 0.0175) =$118.75 2.112.85% 2.12(a) $2500 +$(70 000 0.03) =$4600(b) $4750 +$(40 000 0.025) =$5750 (c) $4750 +$(70 000 0.025) =$6500(d) $6625 +$(275 000 0.02) =$12 125 2.13(a) Commission for $200 000 =$6625 Selling price =$200 000 +$13 375 0.02 =$868 750 (b) $868 750 =$965 278 0.90 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd4 Solutions Manual, Chapter 2 2.14(a) 100 4.49=14.97% or about 15% 29.99 (b) 0.825 $29.99 =$24.74 2.15List price =$1.70=$2.55 0.66667 2.16Amount =$12.50 (1 0.125) 30 =$328.125, say, $328.12 2.17(a) $23 750(b) $24 375 2.18 (c) $24 625 GST =$159.50 (d) $25 000 11 =$14.50 Price excluding GST =$159.50 $14.50 =$145.00 2.19Cost price =$231 2.20(a) Retail price (excluding GST) =$65 1.40 =$91.00 Retail price (including GST) =$91.00 1.10 =$100.10 (b) GST =$107. 80 =$9.80 11 Retail price excluding GST =$107.80 $9.80 =$98 Cost price =$98=$70 1.40 2.21(a) Retail price =$130.00, Cost price =$56.00 (b) Retail price =$162.50, Cost price =$44.80 2.2280% of the list price =$350.Therefore: List price =$350 =$437.50 0.80 2.23(a) Movie typePercentage Comedy34.00 Horror13.33 Drama24.00 Family15.33 Other13.33 Total100 (b) Movie typeMalesFemales Comedy31.0037.43 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd5 Solutions Manual, Chapter 2 Horror17.448.64 Drama24.5023.43 Family10.2521.14 Other16.819.36 Total100100 2.24(a) State/TerritoryPercentage New South Wales32.24 Victoria24.86 Queensland20.27 South Australia7.31 Western Australia10.43 Tasmania2.25 Northern Territory1.02 Australian Capital Territory1.62 (b)Percentage =32.24% +24.86% =57.1% 2.25(a) and (b) Year of birth% increase (Males) % increase (Females) 2015161.240.88 2020210.920.58 2025260.610.46 2050512.911.73 (c) The rate of growth in the life-expectancy will slow down, although still increasing. Note also that the last year interval has a 25-year gap from the previous one. 2.26(a) $3 36.50 =$109.50 (b) $3 218 =$654 (c) ($3 450) +($5 155) =$2125 2.27(a) $60 +(4% of $6870) =$334.80(b) $60 +(4% of $29 990) =$1259.60 (c) $60 +(4% of $12 400) =$556.00 2.28$675 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd6 Solutions Manual, Chapter 2 2.29Total discount =$1000 0.35 =$350 Selling price of stores deal =$1000 $350 =$650 FromExercise2.28,thecustomersowndealmeansa selling price of $675. Hence the customer is $25 better off with the stores deal. 2.30Retail price =$120 Voucher price =$105 Discount price =$102 Hence, the customer should take advantage of discount. 2.31(a) 0 (b) (25410 18200) 19% =$1369.90 (c) 3572 +(125 600 80 000) 37% =$29 620 2.32(a) 0 (b) $3572 +($57 520 $37 000) 32.5% =$10 241 (c) $17 547 +($87 540 $80 000) 37% =$20 336.80 2.33(a) $56 450 0.30 =$16 935 (b) $15 490 0.30 =$4647 (c) $327 900 0.30 =$98 370 2.34(a) $16 250 0.3 =$4875.00(b) $75 320 0.3 =$22 596.00(c) $534 860 0.3 =$160 458.00 2.35Stamp duty =$24 750 2.5% =$618.75 2.36Between $17 901 and $18 000 2.37(a) Marked-up price =1.40 (original price) Discount price =0.90 1.40 (original price) =1.26 (original price) Therefore original price =$252.00 =$200 1.26 (b) Marked-up price =1.40 $200 =$280 2.38(a) Marked-up price =1.40 (original price) Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd7 Solutions Manual, Chapter 2 Discount price =0.60 1.40 (original price) =0.84 (original price) Therefore original price =$252.00 =$300 0.84 (b) Marked-up price =1.40 $300 =$420 2.39(a) Company tax =$70 000 0.30 =$21 000 Personal tax =$3572 +($70 000 $37 000) 32.5% =$14 297 The company tax is greater. (b) Company tax =$80 000 0.30 =$24 000 Personal tax =$17 547 The company tax is greater. (c) Company tax =$90 000 0.30 =$27 000 Personal tax =$17 547+10 000 37% =$21 247 The company tax is greater. 2.40After trial and error for four times: Let i represent income (1)30% i =(i $18 200) 19%($18 200 < i $37 000) (2)30% i =$3672 +(x $37 000) 32.5%($37 000 < i $80 000) (3)30% i =$17 547 +(i $80 000) 37%(($80 000 < i $180 000) (4)30% i =$54 547 +(i $180 000) 45%(i >$180 000) Two answers of (1) and (3) will meet requirement; i1=$31 436.36 i2=$17 2185.71 2.41(a) $3572 +(income $37 000) 32.5% =$7861 Income =$50 196.92 (b) $17 547 +(income 80 000) 37% =$27 113.8 Income =$105 856.22 2.42(a) $135 240 (b) $864 900 2.43(a) $22 500 0.95 =$21 375(b) $22 500 0.97 =$21 825(c) $22 500 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd8 Solutions Manual, Chapter 2 2.44Original account =$1406.50 =$1450 0.97 2.45(a)0.9408$1560=$1467.65(b) 0.9408 $2400= $2257.92(c) 0.9408 $3600 =$3386.88 2.46Original retail price = $1128.96 =$1200 0.96 0.98 2.47Original retail price =$2352=$2500 0.96 0.98 2.48(a) Amount paid =0.96 0.98 $1800 =$1693.44 (b) % discount =100 $106.56 =5.92% $1800 2.49Yes, the percentage discount is the same for any retail price. It can be found by calculating: 100 [1 (0.96 0.98)] =5.92% 2.50 Sales value ($) Return($) for Choice (i)(ii)(iii) Best choice 5000350300280(i) 8000350360400(iii) 10 000350400480(iii) 2.51The best choice for $9 000 is (iii) which earns $440 per week. Choice (i) earns only $350 per week. Over 52 weeks, the extra earnings would have been 52 $90 =$4680. 2.52(a) Weekly sales value =$350 $200 =$7500 0.02 (b) Weekly sales value =$350 $80 =$6750 0.04 2.53Total gross takings =$ 1 307 853 +$2 030 000 =$3 337 853 Percentage due to Australia =$1 307 853100 =39.18% $3 337 853 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd9 Solutions Manual, Chapter 2 2.54Percentage =$100 $8.35 =8.49% $98.35 Average for 15 weeks =$98.35 =$6.557 million 15 This is less than the figure of $8.35 million. 2.55(a)$90 +($25 000 0.025) =$715(b) $90 +($56 000 0.025) =$1490(c) $90 +($125 000 0.025) =$3215 2.56(a) $1800=$72 000 0.025 (b)$2250 =$90 000 0.025 (c)$3900=$156 000 0.025 2.57(a) Stamp duty payable =$1290 +(670 $3.50) =$3635 (b) Stamp duty payable =$8990 +(1920 $4.50) =$17 360 (c) Stamp duty payable =$40 490 +($2350 $5.50) 2.58(a) $75 (b) $960 (c) $690 2.59(a) $0.50(b) $6.16(c) $46.75 2.60(a) $13.75 (b) $9.90 (c) $32.45 2.61Profit =100 $350=23.33% $1500 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd10 Solutions Manual, Chapter 2 2.62(a) $12 700 0.30 =$3810 (b) $47 650 0.30 =$14 295 (c) $1 230 300 0.30 =$369 090 2.63(a) $17 240 0.15 =$2586 (b) $4350 +(43 395 0.30) =$17 368.50 (c) $17 850 +($84 520 0.38) =$49 967.60 2.64(a) $900 +($564 000 0.025) =$15 000 (b) $900 +($1 107 000 0.025) =$28 575 2.65$54 547 +(income $180 000) 45% =$67 250 J errys taxable income =$208 228.89 2.6654 547 +(income $180 000) 45% =$105 125 Rajs taxable income =$292 395.56 2.67Taxable income =$81 600 =$272 000 0.3 2.68Companys taxable income =$476 207.10 =$1 587 357 0.30 2.69(a) $450 0.465 =$209.25 (b) $176 0.465 =$81.84 (c) $2475 0.465 =$1150.88 2.70(a) FBT =$86.00 0.465 =$39.99 (b) FBT =$29.00 0.465 =$13.48 (c) FBT =$54 500.00 0.465 =$25 342.50 2.71(a) No land tax is payable. (b) Land tax =$100 +($458 000 $396 000) 0.016 =$1092 (c) Land tax =$100 +($842 000 $396 000) 0.016 =$7236 2.72(a) As the value is less than the threshold of $396 000, no land tax is payable. (b) The value of $653 000 is ($653 000 $396 000)=$257 000 above the threshold. Land tax payable =$100 +($257 000 0.016) =$4212 (c) The value of $950 000 is ($950 000 $396 000)=$554 000 above the threshold. Land tax payable =$100 +($554 000 x 0.016) =$8964 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd11 Solutions Manual, Chapter 2 2.73J enny pays stamp duty on $12 500 Amount payable =$3 125 =$375 2.74J ason pays stamp duty on $9350 Amount payable =$3 93.5 =$280.50 2.75(a) NSW: $8990 +($4.50 4450) =$29 015 (b) QLD: $10 150 +($4.50 2050) =$19 375 (c) SA: $21 330 +($5.50 2450) =$34 805 (d) VIC: $28 070 +(0.06 $195 000) =$39 770 2.76(a) NSW: $40 490 +($5.50 4005) =$62 517.50 (b) QLD: $29 950 +($5.25 4205) =$52 026.25 (c) SA: $21 330 +($5.50 9005) =$70 857.50 (d) VIC: 0.055 $1 400 500 =$77 027.50 2.77$131.25 =$3500 3.75% 2.788% 150 000 +12% (240 000 150 000) =$22 800 2.79$175 2.80$107.50 2.81$5.31 2.82$4.50 2.83$422.40 2.84(a) Tax payable =$7111.90 Medicare levy =$106.68 (b) Tax payable =$16 416.33 Medicare levy =$246.24 (c) Tax payable =$56 103.55 Medicare levy =$841.55 Medicare levy surcharge =$561.04 Introductory Mathematics and Statistics 6e, John S Croucher, 2013 McGraw-Hill Education (Australia) Pty Ltd12 Solutions Manual, Chapter 2 2.85(a) Company tax payable =0.30 $183 456 =$55 036.80 (b) Company tax payable =0.30 $560 329 =$168 098.70 2.86 The value of $758 000 is ($758 000 $396 000) =$362 000 above the threshold.Land tax payable =$100 +($362 000 0.016) =$5892 2.87Cost price of the slippers =$21.12 =$16 1.32 2.88$11 330 +$5 $1357.25 =$18 116.25 2.895.5% $1 232 500 =$67 787.50 2.90Between $14 401 and $14 500