The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?

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The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?

Givens

• Let Mr. Adam's age be a
• Let Mrs. Benson's age be b
• We're given two equations where sum means we add and difference means we subtract:

1. a + b = 55
2. a - b = 3

Since we have opposite coefficients for b, we can take a shortcut and add equation 1 to equation 2:
(a + a) + (b - b) = 55 + 3

Combining like terms and simplifying, we get:
2a = 58

To solve this equation for a, we type it in our search engine and we get:
a = 29

If a = 29, then we plug this into equation (1) to get:
29 + b = 55
b = 55 - 29
b = 26