SOLUTION: The ages of three brothers, A,B and C, add up to 22. A is 2.5 times older than C. When A was as old as B is today, B is 3 times as old as C. Find their ages.

Question 890159: The ages of three brothers, A,B and C, add up to 22. A is 2.5 times older than C. When A was as old as B is today, B is 3 times as old as C. Find their ages.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
A + B + C = 22, and , from the given.
Now A - B = difference between the ages of A and B.
Hence, A - B years ago,
B - (A - B) = 3[C - (A - B)], from the third sentence.
==> 2A = B + 3C, after simplifying the last equation.
==> 5C = B + 3C, after putting in
==> B = 2C
Then direct substitution gives

==> , or
C = 4 years old,
==> B = 8 years old, and
years old
RELATED QUESTIONS
1. A is as old as the combined age of her two brothers B and C. But C is two years older... (answered by josgarithmetic,ikleyn)

solve this: A is 3 times as old as B and B is 5 years older than C. If B is X years old... (answered by Edwin McCravy)

A is twice as old as B, and C is 5 years younger than B. 3 years from now, A will be 3... (answered by Earlsdon)

The combined ages of A and B are 48 years and A is twice as old as B was when A was half (answered by Edwin McCravy,AnlytcPhil)

A is three as old as B, C is half as old as D and 8 years older than B. In ten years the... (answered by htmentor)

A is 6 years older than B,who is 4 times as old as C. If the sum of their ages is 33,... (answered by Seutip)

A is 20years older than b.5years ago,a was 3 times as old as b.find their present ages. (answered by stanbon)

Thanks in advance for any help in this kind of tricky "Age Problem Equation" as follow:... (answered by ikleyn)

A is 4 years older than b,who is 3 times as old as c.if the sum of their ages is 25 how... (answered by algae132)