# Four times the larger of two numbers is equal to seven times the smaller The sum of the numbers is 22. How do you find the numbers?

##### 2 Answers

The two numbers are 8 and 14.

#### Explanation:

First, let's call our two numbers

Then, we are told, in mathematical terms:

We are also told:

If we solve this equation for n we get:

We can now substitute

We can now substitute

The larger is 14 the smaller is 8

#### Explanation:

Let the larger number be L and the smaller be S

So we know that

1) L+S=22

And

2)4L=7S

From equation 1) we get L=22-S

Substitute this into equation 2) to get 4(22-S)=7S

88-4S=7S

88=11S

S=8. The smaller number is 8

As they total 22 the larger number is 14.

Check: 4x14=7x8. Yes