Two numbers total 66 and have a difference of 24. Find the two numbers?

Question

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Answer 1

Let m and n be the two numbers.

 

Then (1) m + n = 66 and (2) m − n = 24.

 

From (2): * m = n + 24.

 

Substituting into (1):

 

n + 24 + n = 66 or 2n + 24 = 66 or 2n = 66 − 24 = 42 and n = 42/2 = 21.

 

Substituting n = 21 into *: m = 21 + 24 = 45.

 

Checking: 45 + 21 = 66 and 45 − 21 = 24.