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

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Answer 1 · 2017-07-17T18:01:19

See a solution process below:

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 $-6$