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# nossi ch 4 quiz answers

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Answers to the ch 4 quiz

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### nossi ch 4 quiz answers

1. 1. Ch 4 Quiz <ul><ul><ul><li>1. Tell whether each of the following is continuous, discrete or mixed: </li></ul></ul></ul><ul><ul><ul><li>a gallon of ice cream? Continuous because can be divided evenly </li></ul></ul></ul><ul><ul><ul><li>b) a luxury car? Discrete because cannot be divided. </li></ul></ul></ul>
2. 2. <ul><ul><ul><li>2. Pete prefers milk to soda by a ratio of 3 to 1. Pete pays \$4.56 total for a gallon of milk (128 ounces) and a six-pack of soda (72 ounces) </li></ul></ul></ul><ul><ul><ul><li>Total ounces: 128+72 = 200 </li></ul></ul></ul><ul><ul><ul><li>a) What fraction of the total value is the milk?_________ the soda?__________ </li></ul></ul></ul><ul><ul><ul><li>3/4 or 128/200=16/25 1/4 or 72/200=9/25 </li></ul></ul></ul><ul><ul><ul><li>b) How much value would Pete place on the milk in dollars?________ </li></ul></ul></ul><ul><ul><ul><li>Milk=3pts Soda=1 pts </li></ul></ul></ul><ul><ul><ul><li>Milk = 3(128)=384 pts Soda = 1(72)=72 pts </li></ul></ul></ul><ul><ul><ul><li>Value of milk = \$3.84 </li></ul></ul></ul><ul><ul><ul><li>Or \$4.56(3/4) = \$3.42 </li></ul></ul></ul><ul><ul><ul><li>c) How much value would Pete place on the soda in dollars?____________ </li></ul></ul></ul><ul><ul><ul><li>\$.72 using the point value in ouces </li></ul></ul></ul><ul><ul><ul><li>Or \$4.56(1/4) = \$1.14 </li></ul></ul></ul>
3. 3. <ul><ul><ul><li>d) What value would Pete place on 6 ounces of milk and 12 ounces of soda? </li></ul></ul></ul><ul><ul><ul><li>Using pts </li></ul></ul></ul><ul><ul><ul><li>3(6) + 1(12) = 18 + 12 = 30 or 30 cents </li></ul></ul></ul><ul><ul><ul><li>Using dollars </li></ul></ul></ul><ul><ul><ul><li>(6/128)(\$3.42) + (12/72)(\$1.14) = </li></ul></ul></ul><ul><ul><ul><li>.16 + .19 = .35 or 35 cents </li></ul></ul></ul>
4. 4. <ul><ul><ul><li>e) Create two different divisions of the liquid that Pete would think are fair. </li></ul></ul></ul><ul><ul><ul><li>Pete’s total pts = 456. Half of 456 = 228. So a fair division for Pete is a total of 228 pts. </li></ul></ul></ul><ul><ul><ul><li>2 possibilities are: (there are many others) </li></ul></ul></ul><ul><ul><ul><li>Division I : </li></ul></ul></ul><ul><ul><ul><li>Portion 1: 60 oz of milk and 48 oz of soda </li></ul></ul></ul><ul><ul><ul><li>3pts(60oz) = 180 pts for milk </li></ul></ul></ul><ul><ul><ul><li>1pt(48oz) = 48 pts for soda </li></ul></ul></ul><ul><ul><ul><li>Portion 2: 68 oz milk and 24 oz soda </li></ul></ul></ul><ul><ul><ul><li>Division II : </li></ul></ul></ul><ul><ul><ul><li>Portion 1: 70 oz milk and 18 oz soda </li></ul></ul></ul><ul><ul><ul><li>Portion 2: 58 oz milk and 54 oz soda </li></ul></ul></ul><ul><ul><ul><li>**Check pts and total ounces** </li></ul></ul></ul><ul><ul><ul><li>128 ounces of milk and 72 ounces of soda </li></ul></ul></ul>
5. 5. <ul><ul><ul><li>f) Suppose Russell prefers soda to milk in a ratio of 5 pts to 4 pts . For each of the divisions from part (e), determine which portion Russell would choose and why? </li></ul></ul></ul><ul><ul><ul><li>Division I </li></ul></ul></ul><ul><ul><ul><li>5pts(60oz milk) = 300 AND 5(68) = 340 </li></ul></ul></ul><ul><ul><ul><li>4pts(48oz soda) = 192 4(24) = 96 </li></ul></ul></ul><ul><ul><ul><li> total=492 total = 436 </li></ul></ul></ul><ul><ul><ul><li>Russell chooses portion 1 = 492 pts </li></ul></ul></ul><ul><ul><ul><li>Division II </li></ul></ul></ul><ul><ul><ul><li>5 pts(70oz milk) = 350 AND 5(58) = 290 </li></ul></ul></ul><ul><ul><ul><li>4 pts (18oz soda) = 72 4(54) = 216 </li></ul></ul></ul><ul><ul><ul><li>total = 422 total = 506 </li></ul></ul></ul><ul><ul><ul><li>Russell chooses portion 2 = 506 </li></ul></ul></ul>
6. 6. <ul><li>3. A team triathlon consists of a 16-mile run, an 80-mile bike ride, and a 9-mile swim. A team consists of three members. Matt’s running-to-biking-to-swimming ratio is 1 to 4 to 1. Jory’s ratios is 2 to 2 to 1 and Sart’s ratio is 3 to 1 to 4. The events will be divided according to the divide –and-choose method for three players. </li></ul>
7. 7. <ul><ul><ul><li>a) How will each teammate value the entire race, and what would be a fair share according to each person? Complete the following table to help. </li></ul></ul></ul>54.67 164 4 1 3 Sart 67 201 1 2 2 Jorey 115 345 1 4 1 Matt Fair Share Total Pts 9-mile swim 80-mile bike 16-mile run
8. 8. <ul><ul><ul><li>b) Would a 3-mile run, a 10-mile ride, and a 4-mile swim be considered a fair share by any of the three teammates? Justify your answer. (Hint: calculate how many pts this division would equal for each of the 3 players and then compare to your chart above.) </li></ul></ul></ul><ul><li>Matt’s pts: 3(1)+10(4)+4(1) = 47 </li></ul><ul><li>Jarey’s pts: 3(2)+10(2)+1(4) = 30 </li></ul><ul><li>Sart’s pts: 3(3)+10(1)+4(4) = 35 </li></ul><ul><li>Each is less than a fair share </li></ul>
9. 9. <ul><ul><ul><li>4. Three kids, Holly, Harvey, and Hanna, must share a candy bar. For each of the following scenarios, describe the steps in a fair division of the candy bar using the last-diminisher method. </li></ul></ul></ul><ul><ul><ul><li>Holly makes the first cut. Harvey feels the portion is less than a fair share, so he does not make any cuts. Hanna also feels the portion is less than a fair share, so she does not make any cuts. How does this scenario proceed to an end? </li></ul></ul></ul><ul><ul><ul><li>Holly gets first piece (one she cut. The last person to cut gets his/her piece.) Harvey and Hanna use the divide and choose method. </li></ul></ul></ul>
10. 10. <ul><ul><ul><li>b) Holly makes the first cut. Harvey feels the portion is less than a fair share, so he does not make any cuts. Hanna thinks the portion is too big, so she trims the piece. What happens next and how could this scenario end? </li></ul></ul></ul><ul><li>Hanna gets the portion she trimmed. The trimmings are combined with the rest of the candy bar. Holly and Harvey divide and choose. </li></ul>
11. 11. <ul><ul><ul><li>5. Twins Else and Emma receive a painting from their grandmother. Both girls admired the painting often, and the grandmother could not decide which one to give it to. Else believes the painting is worth \$780 and Emma feels it is worth \$835. The girls both want the painting, but they agree to use the method of sealed bids to help them create a fair division. What is the result of the division? Show all work. </li></ul></ul></ul>
12. 12. <ul><li>Emma gets painting and puts \$835 in compensation fund. Each get half of bid: Emma gets 1/2(835)= 417.50 and Else gets 1/2(780) = 390. </li></ul><ul><li>Compensation fund now has </li></ul><ul><li>835 - (417.50+390) = 27.50 which is split evenly between the two girls. </li></ul><ul><li>Else gets \$390 + \$13.75 = \$403.75. </li></ul>
13. 13. <ul><ul><ul><li>6. A couple, Maxine and Dugan, are parting ways and must figure out a way to split up their belongings, including an antique chair, a plasma television, a patio set, a treadmill, and a lawnmower. They agree to abide by the result of the method of sealed bids. Each makes the following bids on each item. </li></ul></ul></ul>
14. 14. <ul><li>Winner is in blue </li></ul>\$490 \$350 Lawnmower \$475 \$560 Treadmill \$250 \$345 Patio set \$4500 \$4200 Plasma television \$245 \$290 Antique chair Dugan’s Bids Maxine’s Bids Items
15. 15. <ul><ul><ul><li>a) How much money is initially placed into the compensation fund? </li></ul></ul></ul><ul><li>290 </li></ul><ul><li>4500 </li></ul><ul><li>345 </li></ul><ul><li>560 </li></ul><ul><li>490 </li></ul><ul><li>6185 total </li></ul>
16. 16. <ul><ul><ul><li>c) What is the final distribution of items and cash? </li></ul></ul></ul><ul><ul><ul><li>Maxinne receives 1/2 of her total bids: </li></ul></ul></ul><ul><ul><ul><li>290 +4200+345+560+350 = 5745 </li></ul></ul></ul><ul><ul><ul><li>1/2 of 5745 = \$2872.50 </li></ul></ul></ul><ul><ul><ul><li>Dugan receives 1/2 of his total bids: </li></ul></ul></ul><ul><ul><ul><li>245+4500+250+475+490 = 5960 </li></ul></ul></ul><ul><ul><ul><li>1/2 of 5960 = \$2980 </li></ul></ul></ul><ul><ul><ul><li>Compensation Fund: </li></ul></ul></ul><ul><ul><ul><li>6185 - (2872.50 + 2980) = \$332.50 which is split evenly between the two: 1/2 332.50 = \$166.25 </li></ul></ul></ul><ul><li>Maxinne gets paid 2872.50+166.25 = 3038.75 but had paid in \$1195 so has a net cash of </li></ul><ul><li>3038.75 - 1195 = \$1843.75 </li></ul>
17. 17. <ul><li>Maxinne gets the chair </li></ul><ul><li>patio set </li></ul><ul><li>treadmill </li></ul><ul><li>\$1843.75 </li></ul><ul><li>Dugan gets the plasma tv </li></ul><ul><li> lawnmower and paid </li></ul><ul><li>Maxinne \$1843.75 </li></ul>
18. 18. <ul><li>I also accepted as correct if dollar values were computed on each item separately. </li></ul><ul><li>Maxinne would get \$2385 </li></ul><ul><li>Dugan would get \$541.25 </li></ul><ul><li>The difference between these two is \$1843.75 which is what Maxinne gets from Dugan. </li></ul>