Question 89982
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>