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

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.

Let the first number be x and;

The second number be y.

So:

x + y = 137 ... (i)

x - y = 17 ... (ii)

Solving this set of simultaneous equations by elimination:

We add (i) to (ii) to get;

2x + 0 = 154

2x = 154, x = 154/2 = 77

y = 77 - 17 = 60

So the first number is 77

And the second number is 60.