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?
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Write some equation
:
"he ratio of sweets in A and B was 7:4 "
{{{A/B}}} = {{{7/4}}}
cross multiply
4A = 7B
B = {{{4/7}}}A
:
"the ratio in B and C was 3:2."
{{{B/C}}} = {{{3/2}}}
2B = 3C
:
"After 36 sweets were from A, the number of sweets in C was 2/3 the number of sweets in A.
C = {{{2/3}}}(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 {{{4/7}}}A
{{{4/7}}}A = A - 36
4A = 7(A - 36); multiplied both sides by 7
4A = 7A - 252
4A - 7A = - 252
-3A = -252
A = {{{(-252)/(-3)}}}
A = +84 sweets in A
:
Find B
B = {{{4/7}}}*84
B = 48 in B
:
Find C
3C = 2B
3C = 2(48)
3C = 96
C = {{{96/3}}}
C = 32 in C
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Total in all 3 containers
84 + 48 + 32 = 164 sweets
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You can confirm this by checking these values in all the equations