SOLUTION: The sum of the ages of Jordan and Christy is 70 years. 8 years ago, Jordan's age was 2 times Christy's age. How old is Jordan now?

Question 1195211: The sum of the ages of Jordan and Christy is 70 years. 8 years ago, Jordan's age was 2 times Christy's age. How old is Jordan now?
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, greenestamps:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
This is too much like another one just solved very recently. Check that one.

Here, question is, find Jordan's age.
y, Jordan
70-y, Christy
"Eight years ago,..."
.
.

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
The sum of the ages of Jordan and Christy is 70 years.
j + c = 70
8 years ago, Jordan's age was 2 times Christy's age.
(j-8) = 2(c-8)
j - 8 = 2c - 16
j = 2c - 16 + 8
j = 2c - 8
in the first equation, replace j with (2c-8)
(2c-8) + c = 70
c + 2c = 70 + 8
3c = 78
c = 78/3
c = 26 yrs is Cristy's age
:
How old is Jordan now?
j = 2c - 8
J = 2(26) - 8
j = 52 - 8
J = 44 yrs is Jordan now
;
:
Check this in the statement
"8 years ago, Jordan's age was 2 times Christy's age."
44 - 8 = 2(26-8)
36 = 2(18)
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

There are dozens of ways to set up and solve a problem like this. The response from the other tutor showed one of them.

I personally would solve the whole thing using logical reasoning and simple arithmetic; but you are probably looking for a formal algebraic solution.

For and algebraic solution, I would still work part of the problem using logical reasoning to make the algebra required to solve the problem easier, before actually setting the problem up using formal algebra.

Since the sum of their ages now is 70, the sum of their ages 8 years ago was 70-2(8) = 70-16 = 54. At that time, Jordan's age was twice Christy's age. So

let x = Christy's age 8 years ago
then 2x = Jordan's age 8 years ago

The sum of their ages 8 years ago was 54:

8 years ago, Christy's age was x=18 and Jordan's age was 2x=36. So now their ages are 18+8=26 and 36+8=44.

ANSWER: Jordan is now 44 years old.

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