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
Dec 3, 2016

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

Dec 3, 2016

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