SOLUTION: The present ages of two brothers are in the ratio of 7:8.Twenty years ago, the ratio of their ages was 9:11. Find the present age of the older brother

Question 1120664: The present ages of two brothers are in the ratio of 7:8.Twenty years ago, the ratio of their ages was 9:11. Find the present age of the older brother
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

Their ages 20 years ago were in the ratio 9:11. So let their ages then be 9x and 11x.

It is a typical way to start work on a problem where a ratio is given.

Then their current ages are 9x+20 and 11x+20; and those ages are in the ratio 7:8. So

Their ages 20 years ago were 9x=36 and 11x=44; their ages now are 36+20=56 and 44+20=64.

Answer: The older brother is now 64.

You should know how to solve a problem like this using formal algebra; however, I always like to encourage students to try to solve a problem informally using logical reasoning -- it's good brain exercise.

In this problem, we know their ages 20 years ago were in the ratio 9:11; that means the older brother's age was a multiple of 11.

And we know that now the ratio of their ages is 7:8, so the older brother's age now is a multiple of 8.

So we only need to find a multiple of 11 which increased by 20 is a multiple of 8.

11+20 = 31 nope...
22+20 = 42 nope...
33+20 = 53 nope...
44+20 = 64 yep!!

The older brother is now 64.
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