Two numbers add up to 102 and the first is 8 bigger than the second. What are the two numbers?

When solving algebraic word problems, we first set a variable to what we are trying to find. Then some "then" statements.

Let x = the smaller number

Then x + 8 = the bigger number

The sum of x and x + 8 is 102.

x + x + 8 = 102

Solve for x.

x + x + 8 = 102

2x + 8 = 102 < - - - Combine like terms

2x = 94 < - - - Subtract each side by 8

x = 47

Then the bigger number is 47 + 8 or 55.

So, the two numbers are 47 and 55.

The correct numbers are 55 and 47, because they have a difference of 8 and a sum of 102.