# The sum of 2 numbers is 25 and their difference is 7. What are the numbers?

Nov 17, 2016

The numbers are 9 and 16.

#### Explanation:

It is possible to solve this problem without using algebra and equations.

One number is 7 more than the other, but they add to 25.

If you subtract the difference of 7 first, you will be left with the sum of two equal numbers.

$25 - 7 = 18$

$18 \div 2 = 9$

The one number is 9 and the other is 7 more than 9, so (9+7 = 16)

The numbers are 9 and 16.

Check: 9+16 = 25#
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You can also use Algebra and only one variable.

Define the numbers first:
Let the smaller number be $x$
The other number is 7 more than x, so it is $\left(x + 7\right)$

The sum of the numbers is 25.

$x + x + 7 = 25$

$2 x + 7 = 25 \text{ } \leftarrow$ subtract 7 from both sides

$2 x = 25 - 7$

$2 x = 18$

$x = 9 \text{ }$ this is the smaller number

The other number is $9 + 7 = 16$