Two numbers total 36 and have a difference of 12. How do you find the two number?

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Answer 1 · 2016-12-06T23:30:33

The two numbers which solve this problem are #12# and #24#

We can write two different equations from the information provided and then use substitution to solve for the two numbers.

First, lets call the numbers we are looking for #m# and #n#.

We now can write:

#m + n = 36# and #m - n = 12#

First, solve the first equation for #m#:

#m + n - n = 36 - n#

#m + 0 = 36 - n#

#m = 36 - n#

Next, we substitute #36 - n# into the second equation for #m# and solve for #n#:

#36 - n - n = 12#

#36 - 2n = 12#

#36 - 2n + 2n - 12 = 12 + 2n - 12#

#36 - 0 - 12 = 0 + 2n#

#24 = 2n#

#24/2 = (2n)/2#

#12 = (cancel(2)n)/cancel(2)#

#12 = n#

Finally, we can substitute #12# for #n# in the solution to the first equation and calculate #m#:

#m = 36 - 12#

#m = 24#