SOLUTION: Peter is four years older than his brother, Paul and their mother is twice Peter's age. if the sum of their ages is 84, how old is each of them?

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Question 305782: Peter is four years older than his brother, Paul and their mother is twice Peter's age. if the sum of their ages is 84, how old is each of them?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let Peter's age = a
Let Paul's age = b
let Mother's age = c
given:
a+%2B+b%2B+c+=+84
a+=+b+%2B+4
c+=+2a
by substitution:
a+%2B+b+%2B+2a+=+84
and, also
a+=+b+%2B+4
b+=+a+-+4
so,
a+%2B+%28a+-+4%29+%2B+2a+=+84
4a+-+4+=+84
4a+=+88
a+=+22
and
c+=+2a
c+=+44
and
b+=+a+-+4
b+=+22+-+4
b+=+18
Peter is 22, Paul is 18, and Mother is 44
check:
a+%2B+b%2B+c+=+84
22+%2B+18+%2B+44+=+84
84+=+84
OK