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

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Answer 1 · 2017-02-25T19:18:12

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

$(1) + (2) \Rightarrow 2 x = 110 \Rightarrow x = 55 .$ $(1)+(2) rArr 2x=110 rArr x=55.$

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

Answer 2 · 2017-02-25T19:54:25

$55$ $55$ and $23$ $23$

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

$a + b$ $a+b$

$a - b$ $a-b$

Then take the sum and difference of these two expressions:

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

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

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

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

$\frac{78 + 32}{2} = \frac{110}{2} = 55$ $(78+32)/2 = 110/2 = 55$

$\frac{78 - 32}{2} = \frac{46}{2} = 23$ $(78-32)/2 = 46/2 = 23$