It was decided that the $15 was a fair price to pay forDel’s share. It was further decided that the 10 logs were worth four times the 15 dogs. How should Albert and Calvert divide the $15?

Question

Al, Cal, and Del went to a cabin one evening. They brought logs for the fire and hot dogs. Al brought 7 logs and 4 dogs. Cal brought 3 logs and 11 dogs. Del brought $15 to cover his share. All the logs were burned up and all the dogs were eaten, with each person eating the same amount. It was decided that the $15 was a fair price to pay forDel’s share. It was further decided that the 10 logs were worth four times the 15 dogs. How should Albert and Calvert divide the $15?

Answer 1

Ok. We have this for input:

Al: 7 logs + 4 dogs

Cal: 3 logs + 11 dogs

Del: $15

There are 4 + 11 = 15 dogs. Split evenly that's 5 dogs per person

There are 7 + 3 = 10 logs. Split evenly that's 10/3 logs per person

We know Del's $15 contribution was considered fair.

Let L = value of a log, D = value of a dog

Del's equation is: 10/3 L + 5 D = $15

If the 10 logs are worth 4 times the 15 dogs, we have 10L = (4 * 15) D, giving us L in terms of D:

10 L = 60 D ; L = 6D

Back to Del's equation, and substitute 6D for L:

10/3 (6D) + 5D = $15

20D + 5D= $15

25D = $15

D = 15/25 = $0.60 Now we have the value of a dog!

Back to Del's equation, use the value of a dog in place of D, and figure out what L is:

10/3 L + 5 ($0.60) = $15

10/3 L + $3 = $15

10/3 L = $12

10 L = $36

L = $36/10 or $3.60

Dogs are worth $0.60 and logs are worth $3.60.

Figure out the value of the items brought by Al and Cal:

Al = 7 * 3.60 + 4*0.60 = 25.20 + 2.40 = $27.60

Cal = 3*3.60 + 11*0.60 = 10.80 + 6.60 = $17.40.

17.40 + 27.60 = $45... so $15 is indeed each boy's share. Subtract the per-person share from the total value each boy brought and you have the amount of Del's $15 each boy receives:

27.60 - 15 = $12.60 for Al

17.40 - 15 = $2.40 for Cal

Voila!