SOLUTION: Tom is 8 years older than Kristina. In 5 years the sum of their ages will be 64. How old is Tom now?

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Question 1174662: Tom is 8 years older than Kristina. In 5 years the sum of their ages will be 64. How old is Tom now?
Found 3 solutions by Boreal, MathTherapy, greenestamps:
Answer by Boreal(15235)   (Show Source):
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K=x
T=x+8
in 5 years they will be x+5 and x+13.
Those two add too 2x+18=64
2x+46
x=23 for K
x+8=31 for Tom
31 years

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

Tom is 8 years older than Kristina. In 5 years the sum of their ages will be 64. How old is Tom now?

Let Tom's age be T
Then Kristina's is: T - 8
We then get: T + T - 8 + 2(5) = 64
2T - 8 + 10 = 64
2T = 62
Tom, or

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

It is good to know how to solve a problem like this using formal algebra. Two other tutors have shown you different ways to do that.

But you can get valuable mental exercise solving the problem informally, using logical reasoning and simple arithmetic.

In 5 years, the sum of the two ages will be 64. That means the sum of their current ages is 54.

Two equal ages with a sum of 54 would be 27 and 27. Starting from there, to get two ages with the same sum of 54 but with a difference of 8 years, add 4 years to one of the ages and subtract 4 years from the other. That gives two ages of 31 and 23.

So their current ages are 23 and 31.