Question

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?

Answer 1

The two numbers are 8 and 14.

Explanation:

First, let's call our two numbers `n` and `m`.

Then, we are told, in mathematical terms:

`4n = 7m`

We are also told:

`n + m = 22`

If we solve this equation for n we get:

`n + m - m = 22 - m`

`n + 0 = 22 - m`

`n = 22 - m`

We can now substitute `22 - m` for `n` in the first equation and solve for `m`:

`4(22 - m) = 7m`

`88 - 4m = 7m`

`88 - 4m + 4m = 7m + 4m`

`88 = 11m`

`88/11 = (11m)/11`

`8 = m`

We can now substitute `8` for `m` in the solution above to calculate `n`:

`n = 22 - 8`

`n = 14`

Answer 2

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