SOLUTION: 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.

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)

RELATED QUESTIONS
please help me with this Adam is 3 times as old as cynthia and Fred is 16 years younger (answered by Anglophile)

Adam is 3 times as old as Cynthia and Fred is 16 yrs. younger than Adam. One year ago,... (answered by ankor@dixie-net.com)

Adam is 3 times as old as Cynthia and Fred is 16 yrs. younger than Adam. One year ago,... (answered by JimboP1977)

1. Adam is 3 times as old as Cynthia and Fred is 16 yrs. younger than Adam. One year ago, (answered by ankor@dixie-net.com)

Adam is three times as old as Cynthia and Fred is sixteen years younger than Adam. One... (answered by ZeratuelX)

Adam is three years younger than Jenn. In one year Jenn will be 3 times as old as Adam... (answered by justasking)

1. Four years ago, Katie was twice as old as Anne was then. In 6 years, Anne will be... (answered by ankor@dixie-net.com)

adam is 5 year younger than eve. in one year eve will be three times the age of adam was... (answered by actuary)

How do i solve using a system of two equations in two variables? Adam is 5 years... (answered by Edwin McCravy)