SOLUTION: Tom is five years older than his sister Melissa, and three times the sum of the ages of these two siblings is two years more than five times the age of Tom. How old is each of thes

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Question 951638: Tom is five years older than his sister Melissa, and three times the sum of the ages of these two siblings is two years more than five times the age of Tom. How old is each of these siblings!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let t = Tom's age
let m = Melissa's age
I think when they refer to "these two siblings" they mean Tom and Mellisa
:
Tom is five years older than his sister Melissa,
t = m + 5
and
three times the sum of the ages of these two siblings is two years more than five times the age of Tom.
3(m + t)= 5t + 2
3m + 3t = 5t + 2
3m = 5t - 3t + 2
3m = 2t + 2
Replace t with (m+5)
3m = 2(m+5) + 2
3m = 2m + 10 + 2
3m - 2m = 12
m = 12 yrs is Melissa's age
then
12 + 5 = 17 yrs is Tom's age
:
:
We can check this in the statement
"three times the sum of the ages of these two siblings is two years more than five times the age of Tom"
3(17+12) = 5(17) + 2
3(29) = 85 + 2