One number is seven less than a second number. Twice the first is 10 more than 6 times the second. How do you find the numbers?

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Answer 1 · 2016-12-06T16:55:53

The first number is $-13$ and the second number is $-6$

Let's let the first number be $n$ and the second number be called $m$ .

Then, from the first sentence we can write:

$n = m - 7$

and from the second sentence we can write:

$2n = 6m + 10$

Substitute $m - 7$ for $n$ in the second equation and solve for $m$ :

$2(m - 7) = 6m + 10$

$2m - 14 = 6m + 10$

$2m - 14 - 2m - 10 = 6m + 10 - 2m - 10$

$-14 - 10 = 6m - 2m$

$-24 = 4m$

$(-24)/4 = (4m)/4$

$m = -6$

Now substitute $-6$ for $m$ in the first equation and calculate $n$ :

$n = -6 - 7$

$n = -13$