SOLUTION: Ken is 64 years younger than Julia. 9 years ago, Julia's age was 3 times Ken's age. How old is Ken now?

Question 1170661: Ken is 64 years younger than Julia. 9 years ago, Julia's age was 3 times Ken's age. How old is Ken now?
Found 3 solutions by akumpo, MathTherapy, greenestamps:
Answer by akumpo(8)   (Show Source): You can put this solution on YOUR website!
We can use system of equations to find the answer. Let k represent Ken's age and j for Julia's age.
k+64=j, because if Ken was 64 years older he would be Julia's age right now.
9 years ago, Ken's age would be k-9. Julia's age would be j-9. 3 times Ken's age then would be 3(k-9). Using distributive property, this equals 3k-27=j-9.
Add 9 to both sides to get 3k-18=j.
Now our two equations are:
k+64=j
3k-18=j
Multiply the first equation by 3 to get:
3k+192=3j
3k-18=j
Now, you can subtract the two equations to get rid of k. This gives you 210=2j. Divide both sides by 2 to get Julia's age now, which is 105. Subtract 105 by 64 to get Ken's age, which is 41.
So Ken is 41 right now, and Julia is 105.
CHECK
Ken is 41 right now. 9 years ago he would be 32. Julia is 105 right now. 9 years ago she would be 96. 32*3 is 96, so this satisfies the second part of the question. As for the first part, 105-41=64, so we know our answer is correct.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Ken is 64 years younger than Julia. 9 years ago, Julia's age was 3 times Ken's age. How old is Ken now?

Let Ken's age be K
Then Julia's is: K + 64
We then get: K + 64 - 9 = 3(K - 9)
K + 55 = 3K - 27
K - 3K = - 27 - 55
- 2K = - 82
Ken's age, or
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

Here is a completely different way to solve this kind of problem....

Start with the fact that 9 years ago Julia's age was 3 times Ken's age. We can then say that their ages 9 years ago were 3x and x.

The difference between their ages 9 years ago is then 3x-x=2x. But we know the difference between their ages is (and always was/will be) 64.

So 2x=64; x=32; and their ages 9 years ago were 3x=96 and x=32.

Since that was 9 years ago, Ken's age is now 32+9=41.

ANSWER: Ken is 41

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