SOLUTION: Sweets were placed in 3 containers, A, B, and C. The ratio of sweets in A and B was 7:4 and the ratio in B and C was 3:2. After 36 sweets were from A, the number of sweets in C was

Algebra ->  Proportions -> SOLUTION: Sweets were placed in 3 containers, A, B, and C. The ratio of sweets in A and B was 7:4 and the ratio in B and C was 3:2. After 36 sweets were from A, the number of sweets in C was      Log On


   

Question 542482: Sweets were placed in 3 containers, A, B, and C. The ratio of sweets in A and B was 7:4 and the ratio in B and C was 3:2. After 36 sweets were from A, the number of sweets in C was 2/3 the number of sweets in A. What was the total number of sweets left in the three containers?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Sweets were placed in 3 containers, A, B, and C.
The ratio of sweets in A and B was 7:4 and the ratio in B and C was 3:2.
After 36 sweets were from A, the number of sweets in C was 2/3 the number of sweets in A.
What was the total number of sweets left in the three containers?
:
Write some equation
:
"he ratio of sweets in A and B was 7:4 "
A%2FB = 7%2F4
cross multiply
4A = 7B
B = 4%2F7A
:
"the ratio in B and C was 3:2."
B%2FC = 3%2F2
2B = 3C
:
"After 36 sweets were from A, the number of sweets in C was 2/3 the number of sweets in A.
C = 2%2F3(A-36)
3C = 2(A-36); multiplied both sides by 3
3C = 2A - 72
Replace 3C with 2B
2B = 2A - 72
Simplify, divide by 2
B = A - 36
Replace B with 4%2F7A
4%2F7A = A - 36
4A = 7(A - 36); multiplied both sides by 7
4A = 7A - 252
4A - 7A = - 252
-3A = -252
A = %28-252%29%2F%28-3%29
A = +84 sweets in A
:
Find B
B = 4%2F7*84
B = 48 in B
:
Find C
3C = 2B
3C = 2(48)
3C = 96
C = 96%2F3
C = 32 in C
:
Total in all 3 containers
84 + 48 + 32 = 164 sweets
:
:
You can confirm this by checking these values in all the equations