Question 89982: Adam is 3 times as old as Cynthia and Fred is 16 yrs. younger than Adam. One year ago, Adam's age was twice the sum of Cynthia's and Fred's age. Find their present age.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A = Adams age now; C = Cynthia's name now; F = Fred's name now.
:
Write an equation for each statement:
:
"Adam is 3 times as old as Cynthia"
A = 3C
:
"Fred is 16 yrs. younger than Adam."
F = A - 16
:
"One year ago, Adam's age was twice the sum of Cynthia's and Fred's age."
(A-1) = 2((C-1) + (F-1))
A - 1 = 2(C + F - 1 - 1)
A - 1 = 2(C + F - 2)
A - 1 = 2C + 2F - 4
A = 2C + 2F - 4 + 1
A = 2C + 2F - 3
:
At this point we could make C and F in terms of A
A = 3C
Therefore:
C = (A/3
and
F = (A-16)
:
Find their present age.
Using equation: A = 2C + 2F - 3, substitute (A/3) for C and (A-16) for F
:
A = 2(A/3) + 2(A-16) - 3
A = 2A/3 + 2A - 32 - 3
A = 2A/3 + 2A - 35
:
Multiply equation by 3 to get rid of the fraction, you then have:
3A = 2A + 6A - 105
3A = 8A - 105
105 = 8A - 3A
105 = 5A
A = 105/5
A = 21 is Adams age now
:
C = 21/3 = 7 is Cynthia's age now
:
F = 21 - 16 = 5 is Fred's age now
:
:
Use the statement, "One year ago, Adam's age was twice the sum of Cynthia's and Fred's age." to check our solution:
20 = 2(6 + 4)
:
A kind of round about way, hope this helps you>
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