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#