The sum of two numbers is 95, and their difference is 61. What are the two numbers?

Let’s call:

\( first\#=x \)

\( second\#=y \)

then

when we have a SUM, we have PLUS and when we have a DIFFERENCE, we have MINUS. Let’s go then.

\( \begin{matrix}x+y&=&95\\x-y&=&61\end{matrix} \)

now we can sum all the rows then we got it. (This is the other way to solved this question)

\( x+y+(x-y)=95+61 \)

\( x+y+x-y=156 \)

\( 2x=156 \)

\( \boxed{x=78} \)

now we can replace this value at first or at second row, you just need to pick up one.

I’ll choose the second one

\( x-y=61 \)

\( 78-y=61 \)

\( y=78-61 \)

\( \boxed{y=17} \)

\( \boxed{\boxed{\begin{matrix}x&=&78\\y&=&17\end{matrix}}} \)

\( \left \{ {x+y=95} \atop {x-y=61} \right. \\ 2x=156\\ x= \frac{156}{2} \\ \x=78\\ \y=95-y \\ y=95-78 \\ y=17 \)

First number 78, and the second is 17.


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