Alan, Bill and Carl shared \$372. After Alan spend 2/ 5 of his share, Bill spent 1 /2 of his share and Carl spent 1/3 of his share, the boys found they had the same amount of money left.

(a) What is the ratio of Alan's share to Bill's share to Carl's share?

(b) How much did they spend altogether?

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2. 👎 0
3. 👁 104
1. a + b + c = 372
what is left to each = 1-fraction spent
(3/5) a = (1/2)b = (2/3) c

(a) common denominator is 30
18a = 15 b = 20 c
so a/b = 15/18 = 5/6
a/c = 20/18 = 10/9
b/c = 20/15 = 4/3

(b)
a = 10 c/9
b = 4c/3

a + b + c = 372
10c/9 + 4c/3 + c = 372

10 c/9 + 12 c/9 + 9 c/9 = 372
31 c = 9*372
c = 108

You can take it from there I think

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2. 👎 0
posted by Damon
2. By the way - grade 5 ??

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2. 👎 0
posted by Damon
3. A, B, C are the initial amounts.

then
3/5 A= 1/2 B = 2/3 C then
A=10/9 C
B=4/3 C
but A+B+C=372 so
10/9 C+ 4/3 C+ C=372
10C+12C+9C=9*372
31C=9*372

C= you do it. From this, figure A, and B.

Then, ratios are A/B, A/C, and B/C

how much did they spend? go back to the problem, and do that calculation.

check my logic

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2. 👎 0

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