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nossi ch 4 quiz answers

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Answers to the ch 4 quiz

Answers to the ch 4 quiz

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  • 1. Ch 4 Quiz
        • 1. Tell whether each of the following is continuous, discrete or mixed:
        • a gallon of ice cream? Continuous because can be divided evenly
        • b) a luxury car? Discrete because cannot be divided.
  • 2.
        • 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)
        • Total ounces: 128+72 = 200
        • a) What fraction of the total value is the milk?_________ the soda?__________
        • 3/4 or 128/200=16/25 1/4 or 72/200=9/25
        • b) How much value would Pete place on the milk in dollars?________
        • Milk=3pts Soda=1 pts
        • Milk = 3(128)=384 pts Soda = 1(72)=72 pts
        • Value of milk = $3.84
        • Or $4.56(3/4) = $3.42
        • c) How much value would Pete place on the soda in dollars?____________
        • $.72 using the point value in ouces
        • Or $4.56(1/4) = $1.14
  • 3.
        • d) What value would Pete place on 6 ounces of milk and 12 ounces of soda?
        • Using pts
        • 3(6) + 1(12) = 18 + 12 = 30 or 30 cents
        • Using dollars
        • (6/128)($3.42) + (12/72)($1.14) =
        • .16 + .19 = .35 or 35 cents
  • 4.
        • e) Create two different divisions of the liquid that Pete would think are fair.
        • Pete’s total pts = 456. Half of 456 = 228. So a fair division for Pete is a total of 228 pts.
        • 2 possibilities are: (there are many others)
        • Division I :
        • Portion 1: 60 oz of milk and 48 oz of soda
        • 3pts(60oz) = 180 pts for milk
        • 1pt(48oz) = 48 pts for soda
        • Portion 2: 68 oz milk and 24 oz soda
        • Division II :
        • Portion 1: 70 oz milk and 18 oz soda
        • Portion 2: 58 oz milk and 54 oz soda
        • **Check pts and total ounces**
        • 128 ounces of milk and 72 ounces of soda
  • 5.
        • 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?
        • Division I
        • 5pts(60oz milk) = 300 AND 5(68) = 340
        • 4pts(48oz soda) = 192 4(24) = 96
        • total=492 total = 436
        • Russell chooses portion 1 = 492 pts
        • Division II
        • 5 pts(70oz milk) = 350 AND 5(58) = 290
        • 4 pts (18oz soda) = 72 4(54) = 216
        • total = 422 total = 506
        • Russell chooses portion 2 = 506
  • 6.
    • 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.
  • 7.
        • 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.
    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.
        • 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.)
    • Matt’s pts: 3(1)+10(4)+4(1) = 47
    • Jarey’s pts: 3(2)+10(2)+1(4) = 30
    • Sart’s pts: 3(3)+10(1)+4(4) = 35
    • Each is less than a fair share
  • 9.
        • 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.
        • 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?
        • 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.
  • 10.
        • 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?
    • Hanna gets the portion she trimmed. The trimmings are combined with the rest of the candy bar. Holly and Harvey divide and choose.
  • 11.
        • 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.
  • 12.
    • 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.
    • Compensation fund now has
    • 835 - (417.50+390) = 27.50 which is split evenly between the two girls.
    • Else gets $390 + $13.75 = $403.75.
  • 13.
        • 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.
  • 14.
    • Winner is in blue
    $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.
        • a) How much money is initially placed into the compensation fund?
    • 290
    • 4500
    • 345
    • 560
    • 490
    • 6185 total
  • 16.
        • c) What is the final distribution of items and cash?
        • Maxinne receives 1/2 of her total bids:
        • 290 +4200+345+560+350 = 5745
        • 1/2 of 5745 = $2872.50
        • Dugan receives 1/2 of his total bids:
        • 245+4500+250+475+490 = 5960
        • 1/2 of 5960 = $2980
        • Compensation Fund:
        • 6185 - (2872.50 + 2980) = $332.50 which is split evenly between the two: 1/2 332.50 = $166.25
    • Maxinne gets paid 2872.50+166.25 = 3038.75 but had paid in $1195 so has a net cash of
    • 3038.75 - 1195 = $1843.75
  • 17.
    • Maxinne gets the chair
    • patio set
    • treadmill
    • $1843.75
    • Dugan gets the plasma tv
    • lawnmower and paid
    • Maxinne $1843.75
  • 18.
    • I also accepted as correct if dollar values were computed on each item separately.
    • Maxinne would get $2385
    • Dugan would get $541.25
    • The difference between these two is $1843.75 which is what Maxinne gets from Dugan.
  • 19.