The difference of two numbers is 3. Their sum is 13. How do you find the numbers?

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Answer 1 · 2017-01-06T04:35:53

The two numbers are $8$ $8$ and $5$ $5$ .

Consider the two numbers as $x$ $x$ and $y$ $y$ . From the given data, we write:

$x - y = 3$ $x-y=3$
$x + y = 13$ $x+y=13$

From the first equation, we determine a value for $x$ $x$ .

$x - y = 3$ $x-y=3$

Add $y$ $y$ to both sides.

$x = y + 3$ $x=y+3$

In the second equation, substitute $x$ $x$ with $(y + 3)$ $color(red)((y+3))$ .

$x + y = 13$ $x+y=13$

$(y + 3) + y = 13$ $color(red)((y+3))+y=13$

Open the brackets and simplify.

$y + 3 + y = 13$ $color(red)(y+3)+y=13$

$2 y + 3 = 13$ $2y+3=13$

Subtract $3$ $3$ from each side.

$2 y = 10$ $2y=10$

Divide both sides by $2$ $2$ .

$y = 5$ $y=5$

In the first equation, substitute $y$ $y$ with $5$ $color(blue)(5)$ .

$x - y = 3$ $x-y=3$

$x - 5 = 3$ $x-color(blue)(5)=3$

Add $5$ $5$ to each side.

$x = 8$ $x=8$