SOLUTION: The ratio of age of a man and his wife is 4:3 ...at the time of marriage, the ratio was 5:3 and after 4 yrs the ratio will become 9:7... How many yrs ago were they married?

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Question 977409: The ratio of age of a man and his wife is 4:3 ...at the time of marriage, the ratio was 5:3 and after 4 yrs the ratio will become 9:7... How many yrs ago were they married?



Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio of age of a man and his wife is 4:3 ...at the time of marriage, the ratio was 5:3 and after 4 yrs the ratio will become 9:7... How many yrs ago were they married?
Let the number of years ago they were married be y years ago.

The ratio of age of a man and his wife is 4:3
So there is some number k, so that the man's age is now 4k 
and the wife's age is now 3k 

...at the time of marriage, the ratio was 5:3
%284k-y%29%2F%283k-y%29%22%22=%22%225%2F3

3%284k-y%29%22%22=%22%225%283k-y%29

12k-3y%22%22=%22%2215k-5y

2y%22%22=%22%223k

and after 4 yrs the ratio will become 9:7...
%284k%2B4%29%2F%283k%2B4%29%22%22=%22%229%2F7

7%284k%2B4%29%22%22=%22%229%283k%2B4%29

28k%2B28%22%22=%22%2227k%2B36

k%22%22=%22%228

Substitute that in 

2y%22%22=%22%223k
2y%22%22=%22%223%288%29
2y%22%22=%22%2224
y%22%22=%22%2212

Answer:  12 years ago.

Checking:

The man is 4k = 4(8) = 32
The wife is 3k = 3(8) = 24

The ratio of age of a man and his wife is 4:3
32/24 = 4/3, that checks.

...at the time of marriage, the ratio was 5:3
They married 12 years ago when he was 20 and she was only 12. (WOW!)

20/12 = 5/3, that checks.  (WOW!!)

and after 4 yrs the ratio will become 9:7...
He will be 36 and she will be 28

36/28 = 9/7, that checks.

That's correct but I think it's terrible that your teacher would assign 
a problem that implies that a girl was married at age 12, even if it is
only a math problem !!!  

Edwin