SOLUTION: Luke is five years younger than Jason. Two year ago, the sum of their ages was 33. How old are they?

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Question 1164622: Luke is five years younger than Jason. Two year ago, the sum of their ages was 33. How old are they?
Answer by greenestamps(13200) About Me  (Show Source):
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A typical setup using formal algebra....

x = Jason's age
x-5 = Luke's age

x-2 = Jason's age 2 years ago
x-5-2 = x-7 = Luke's age 2 years ago

The sum of their ages 2 years ago was 33:

%28x-2%29%2B%28x-7%29+=+33

Solve using basic algebra....

Informally....

2 years ago, the sum of their ages was 33; so now the sum of their ages is 37.

Add 5 years to Luke's age, so that their ages are the same; the sum of their ages is now 37+5 = 42. So Jason is 42/2 = 21.

Now subtract those "extra" 5 years from Luke's age to find that Luke is 21-5 = 16.

Answer: Their current ages are 21 and 16.