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 1184389: 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 had to the number of stickers Benedict had to the number of stickers Caleb had.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The ratio of the number of stickers Aaron had to the total number of stickers Benedict and Caleb had was 2:3.
a%2F%28b%2Bc%29 = 2%2F3
cross multiply
3a = 2(b+c)
3a = 2b + 2c
3a - 2b - 2c = 0
:
The ratio of the number of stickers Benedict had to the total number of stickers Aaron and Caleb had was 4:5.
b%2F%28a%2Bc%29 = 4%2F5
cross multiply
5b = 4(a+c)
5b = 4a + 4c
5b - 4a - 4c = 0
rearrange
-4a + 5b - 4c = 0
:
Add these equations
-4a+ 5b - 4c = 0
3a - 2b - 2c = 0
------------------
-a + 3b - 6c = 0
therefore
a = 3b - 6c
replace a with (3b-6c) in the first equation
3(3b-6c) = 2b + 2c
9b - 18c = 2b + 2c
9b - 2b - 18c - 2c = 0
7b - 20c = 0
7b = 20c
The first integer solution to this equation: b=20 and c=7
:
With these values find a using the first equation
3a = 2(20+7)
3a = 54
a = 54/3
a = 18
Find the ratio of the number of stickers Aaron had to the number of stickers Benedict had to the number of stickers Caleb had.
that would be: 18:20:7