SOLUTION: The ratio of the number of stickers Aaron had to the total number of stickers Benedict and Caleb had was 2:3. The ratio of the number of stickers Benedict had to the total number o

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The ratio of the number of stickers Aaron had to the total number of stickers Benedict and Caleb had was 2:3. The ratio of the number of stickers Benedict had to the total number o      Log On


   

Question 1186390: The ratio of the number of stickers Aaron had to the total number of stickers Benedict and Caleb had was 2:3. The ratio of the number of stickers Benedict had to the total number of stickers Aaron and Caleb had was 4:5. Find the ratio of the number of stickers Aaron has to the number of stickers Benedict had to the number of stickers Caleb had.
Answer by greenestamps(13206) About Me  (Show Source):
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The number Aaron had was 2/3 the number Benedict and Caleb had together:

(1) A=%282%2F3%29%28B%2BC%29

The number Aaron and Caleb had together was 5/4 the number Benedict had:

(2) A%2BC=%285%2F4%29%28B%29

Substitute (1) into (2):

%282%2F3%29%28B%2BC%29%2BC=%285%2F4%29%28B%29
%282%2F3%29B%2B%285%2F3%29C=%285%2F4%29B
%285%2F3%29C=%285%2F4%29B-%282%2F3%29B
%285%2F3%29C=%287%2F12%29B

Multiply by 12 to clear fractions:

20C=7B
B%2FC=20%2F7

Let B=20x and C=7x and substitute in (1):

A=%282%2F3%29%2820x%2B7x%29
A=%282%2F3%2927x
A=18x

A:B:C = 18x:20x:7x

ANSWER: A:B:C = 18:20:7