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

1 Answer
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#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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 #(x+7)#

The sum of the numbers is 25.

#x+x+7 = 25#

#2x +7 = 25" "larr# subtract 7 from both sides

#2x = 25-7#

#2x = 18#

#x = 9" "# this is the smaller number

The other number is #9+7 = 16#