SOLUTION: the ratio of the ages of a husband and his wife is 4:3. after 4 years this ratio will be 9:7. if at the time of the marriage the ratio was 5:3, then how many years ago thy got marr

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Question 715609: the ratio of the ages of a husband and his wife is 4:3. after 4 years this ratio will be 9:7. if at the time of the marriage the ratio was 5:3, then how many years ago thy got married?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
husband --------- x
wife = y
x%2Fy=4%2F3%29
3x-4y=0...................(1)

after 4 years
(x+4)/(y+4) =9/7
7(x+4)=9(y+4)
7x+28=9y+36
7x-9y=8..............(2
x= husband's age
y= wife's age

3 x -4 y = 0 .............1
Total value
7 x -9 y = 8 .............2
Eliminate y
multiply (1)by -9
Multiply (2) by 4
-27 x 36 y = 0
28 x -36 y = 32
Add the two equations
1 x = 32
/ 1
x = 32
plug value of x in (1)
3 x -4 y = 0
96 -4 y = 0
-4 y = 0 -96
-4 y = -96
y = 24
x= 32 husband's age
y= 24 wife's age
)

let a be the years ago they married
(x-a)/(y-a) =5/3
(32-a)/(24-a) =5/3
3(32-a)=5(24-a)
96-3a=120-5a
2a=24
a=12
They got married 12 years ago