The sum of two numbers is 78. Their difference is 32. What are these numbers?

2 Answers
Feb 25, 2017

#(1) : x+y=78" & "(2) : x-y=32, (x gt y).#

#(1)+(2) rArr 2x=110 rArr x=55.#

& then, by #(1), y=78-55=23.#

Feb 25, 2017

Answer:

#55# and #23#

Explanation:

Given two numbers #a# and #b#, take their sum and difference:

#a+b#

#a-b#

Then take the sum and difference of these two expressions:

#(a+b)+(a-b) = 2a#

#(a+b)-(a-b) = 2b#

Notice that we get back to the two numbers we started with, but doubled.

So with #78# and #32#, form their sum and difference and halve the results to get the two original numbers:

#(78+32)/2 = 110/2 = 55#

#(78-32)/2 = 46/2 = 23#