SOLUTION: After 6 years the ratio of age of X and Y will be 5:6. Before 6 years it was 3:4. Find the age of younger one.

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Question 680219: After 6 years the ratio of age of X and Y will be 5:6. Before 6 years it was 3:4. Find the age of younger one.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
"After 6 years the ratio of age of X and Y will be 5:6."
%28%28x%2B6%29%29%2F%28%28y%2B6%29%29 = 5%2F6
Cross multiply
6(x+6) = 5(y+6)
6x + 36 = 5y + 30
6x - 5y = 30 - 36
6x - 5y = -6
:
" Before 6 years it was 3:4."
%28%28x-6%29%29%2F%28%28y-6%29%29 = 3%2F4
cross multiply
4(x-6) = 3(y-6)
4x - 24 = 3y - 18
4x - 3y = -18 + 24
4x - 3y = 6
:
Multiply the 1st equation by -3, the 2nd equation by 5
-18x + 15y = 18
20x - 15y = 30
-----------------adding eliminates y, findx
2x = 48
x = 24 yrs old
:
find y
4x - 3y = 6
4(24) - 3y = 6
96 - 3y = 6
-3y = 6 - 96
-3y = -90
y = -90/-3
y = 30 yrs old
:
Find the age of younger one. 24 yrs
:
:
Check solution in the 1st statement;
"After 6 years the ratio of age of X and Y will be 5:6."
%28%28x%2B6%29%29%2F%28%28y%2B6%29%29 = 5%2F6
%28%2824%2B6%29%29%2F%28%2830%2B6%29%29 = 5%2F6
30%2F36 = 5%2F6