Question

Two numbers add up to 137 and the first is 17 bigger than the second. What are the two numbers?

Answer 1

If a and b are the numbers, a+b=137; and a=b+17.

So a-b=17. Add two equations together: (a+b)+(a-b)=137+17=154 and 2a=154, making a=77.

If a=77 b must be 137-77=60.

The two numbers are 77 and 60.

Answer 2

Let two numbers are A and B
A + B = 137
A = B + 17

Substitute the known value of A from the second equation into the first.
(B+17) + B = 137

Add
2B + 17 = 137

Subtract 17 from each side
2B = 120

Divide
B = 60

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