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
smendyka
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#

Annie
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

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