SOLUTION: 1. 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 Chyntia's & Fred's age. Find their present age.

Question 240005: 1. 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 Chyntia'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 equation for each statement:
:
"1. Adam is 3 times as old as Cynthia "
A = 3C
or
C = A
;
" Fred is 16 yrs. younger than Adam."
F = A - 16
:
One year ago, Adam's age was twice the sum of Chyntia's & Fred's age."
A - 1 = 2(C-1 + F-1)
Simplify and combine as much as we can
A - 1 = 2(C + F - 2)
A - 1 = 2C + 2F - 4
A = 2C + 2F - 4 + 1
A = 2C + 2F - 3
From the 1st two equations; replace C with A, replace F with (A-16)
A = 2(A) + 2(A-16) - 3
A = A + 2A - 32 - 3
A = A + 2A - 35
35 = 2A - A
35 = 1A
As an improper fraction
35 = A
Divide 35 by (5/3)
A = 35 *
A = 7(3)
A = 21 yrs old is Adam
:
Find their present age.
C = *21
C = 7 yrs is Cynthia
and
F = 21 - 16
F = 5 yrs is Fred
;
:
Check solutions in the statement:
"One year ago, Adam's age was twice the sum of Cynthia's & Fred's age."
20 = 2(6 + 4)
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