SOLUTION: Clyde, Jeffrey and Geneross are three brothers. The sum of their ages five years ago is 13/25 of the sum of their ages three years from now. If Geneross’s age is the same as the

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Question 1185056: Clyde, Jeffrey and Geneross are three brothers. The sum of their ages five years ago is 13/25 of the
sum of their ages three years from now. If Geneross’s age is the same as the age of Clyde five years
ago and Clyde is two years older than Jeffrey. How old are they ten years from now?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
c Clyde
j Jeffry
g Geneross

system%28c%2Bj%2Bg-15=%2813%2F25%29%28c%2Bj%2Bg%2B9%29%2Cg=c-5%2Cc=j%2B2%29

system%2825c%2B25j%2B25g-15%2A25=13c%2B13j%2B13g%2B117%2Cg=c-5%2Cj=c-2%29

system%2812c%2B12j%2B12g=15%2A25%2B117%2Cg=c-5%2Cj=c-2%29

system%2812c%2B12j%2B12g=492%2Cg=c-5%2Cj=c-2%29

system%28c%2Bj%2Bg=41%2Cg=c-5%2Cj=c-2%29

Substitute for g and j into the first equation and have one equation all in one single variable, c.
highlight_green%28c%2B%28c-2%29%2B%28c-5%29=41%29
.
.
.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The difference between the sum of their ages 5 years ago and the sum of their ages 3 years from now is 3*8=24.

A mental path for the first part of the problem is to rewrite the given fraction 13/25 as an equivalent fraction in which the difference between numerator and denominator is 24. The difference between 13 and 25 is 12, so we can double numerator and denominator: 13/25 = 26/50.

So the sum of their ages 5 years ago was 26 and the sum of their ages 3 years from now is 50. That means the sum of their ages now is 41.

Geneross's age is the same as Clyde's age 5 years ago, so Geneross is 5 years younger than Clyde.

Clyde is 2 years older than Jeffrey, so Jeffrey is 2 years younger than Clyde.

x = Clyde
x-5 = Geneross
x-2 = Jeffrey

The sum of their current ages is 41:

x%2Bx-5%2Bx-2=41
3x-7=41
3x=48
x=16

Their current ages are
Clyde: x=16
Geneross: x-5=11
Jeffrey: x-2=14

ANSWER: Their ages 10 years from now will be
Clyde: 16+10=26
Geneross: 11+10=21
Jeffrey: 14+10=24