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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