Question

The sum of two numbers is 17 and their difference is 29. What are the two numbers?

Answer 1

See a solution process below:

Explanation:

First, let's give the two numbers a name:

Number 1: we will call: `n`

Number 2: we will call: `m`

From the information in the problem we can write these two equations:

Equation 1: `n + m = 17`

Equation 2: `n - m = 29`

Step 1 Solve the first equation for `n`:

`n + m = 17`

`n + m - color(red)(m) = 17 - color(red)(m)`

`n + 0 = 17 - m`

`n = 17 - m`

Step 2 Substitute `(17 - m)` for `n` in the second equation and solve for `m`:

`n - m = 29` becomes:

`(17 - m) - m = 29`

`17 - 1m - 1m = 29`

`17 + (-1 - 1)m = 29`

`17 + (-2)m = 29`

`17 - 2m = 29`

`-color(red)(17) + 17 - 2m = -color(red)(17) + 29`

`0 - 2m = 12`

`-2m = 12`

`(-2m)/color(red)(-2) = 12/color(red)(-2)`

`(color(red)(cancel(color(black)(-2)))m)/cancel(color(red)(-2)) = -6`

`m = -6`

Step 3 Substitute `-6` for `m` in the solution to the first equation at the end of Step 1 and calculate `n`:

`n = 17 - m` becomes:

`n = 17 - (-6)`

`n = 17 + 6`

`n = 23`

The Two Numbers Are: `23` and `-6`