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?

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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?

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Answer 1 · 2016-12-03T12:18:47

The two numbers are 8 and 14.

Explanation:

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

Then, we are told, in mathematical terms:

$4 n = 7 m$ $4n = 7m$

We are also told:

$n + m = 22$ $n + m = 22$

If we solve this equation for n we get:

$n + m - m = 22 - m$ $n + m - m = 22 - m$

$n + 0 = 22 - m$ $n + 0 = 22 - m$

$n = 22 - m$ $n = 22 - m$

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

$4 (22 - m) = 7 m$ $4(22 - m) = 7m$

$88 - 4 m = 7 m$ $88 - 4m = 7m$

$88 - 4 m + 4 m = 7 m + 4 m$ $88 - 4m + 4m = 7m + 4m$

$88 = 11 m$ $88 = 11m$

$\frac{88}{11} = \frac{11 m}{11}$ $88/11 = (11m)/11$

$8 = m$ $8 = m$

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

$n = 22 - 8$ $n = 22 - 8$

$n = 14$ $n = 14$

Answer 2 · 2016-12-03T12:26:55

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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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

Explanation:

Explanation:

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