Question 97319: Adam is 3 times as old as Cynthia and Fred is 16 years younger than Adam. One year ago, Adam's age was twice the sum of Cynthia's & Fred's age. Find their present age.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Write an expression or equation for each statement
:
Adam is 3 times as old as Cynthia
A = 3C
Or
C = A/3
:
Fred is 16 years younger than Adam.
F = (A-16)
:
One year ago, Adam's age was twice the sum of Cynthia's & Fred's age.
(A-1) = 2((C-1) + (F-1))
(A-1) = 2(C + F - 2)
A-1 = 2C + 2F - 4
A = 2C + 2F - 4 + 1
A = 2C + 2F - 3
:
Find their present age.
:
Substitute for C & F, from the 1st and 2nd equation:
A = 2(A/3) + 2(A-16) - 3
A = (2A/3) + 2A - 32 - 3
A = (2A/3) + 2A - 35
:
Get rid of the denominator, mult equation by 3
3A = 2A + 6A - 105
3A = 8A - 105
3A - 8A = -105
-5A = -105
A = -105/-5
A = 21 yrs is Adams age now
:
C = 21/3 = 7 yrs old is Cynthia now
:
F = 21 - 16 = 5 yrs old is Fred now
:
:
Check solution using:
"One year ago, Adam's age was twice the sum of Cynthia's & Fred's age."
20 = 2(6 + 4)
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