The sum of two numbers is 80. lf three times the smaller number is subtracted from the larger number, the result is 16. How do you find the two numbers?

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Answer 1 · 2016-12-01T16:32:44

#x = 64# and #y = 16#

First, let's call the two numbers we are looking for #x# and #y# and say #x# is the larger number.

From the problem we know:

#x + y = 80#

We also know:

#x - 3y = 16#

Solving the first equation for #x# gives:

#x + y - y = 80 - y#

#x = 80 - y#

We can now substitute #80 - y# for #x# in the second equation and solve for #y#:

#80 - y - 3y = 16#

#80 - 4y = 16#

#80 - 80 - 4y = 16 - 80#

#-4y = -64#

#(-4y)/-4 = (-64)/(-4)#

#y = 16#

Finally, we can substitute #16# for #y# in the solution to the first equation:

#x = 80 - 16#

#x = 64#