The sum of two numbers is 48, their difference is 24. What are the numbers?

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Answer 1 · 2017-02-13T03:17:04

The two numbers are 12 and 36

First, let's name the two numbers $n$ and $m$ .

Then we can write:

$n + m = 48$

and

$n - m = 24$

Step 1) Solve the first equation for $n$ :

$n + m = 48$

$n + m - color(red)(m) = 48 - color(red)(m)$

$n + 0 = 48 - m$

$n = 48 - m$

Step 2) Substitute $48 - m$ for $n$ in the second equation and solve for $m$ :

$n - m = 24$ becomes:

$48 - m - m = 24$

$48 - 2m = 24$

$-color(red)(48) + 48 - 2m = -color(red)(48) + 24$

$0 - 2m = -24$

$-2m = -24$

$(-2m)/color(red)(-2) = (-24)/color(red)(-2)$

$(color(red)(cancel(color(black)(-2)))m)/cancel(color(red)(-2)) = 12$

$m = 12$

Step 3) Substitute $12$ for $m$ in the solution to the first equation at the end of Step 1 and calculate $n$ :

$n = 48 - m$ becomes:

$n = 48 - 12$

$n = 36$