Question

find the value of two numbers if their sum is 751 and their difference is 255

Answer 1

we can write the sum of two numbers like this:

$x+y$

and their difference like this:

$x-y$

then,in this case, we have the following system of equations:

$\begin{gathered} x+y=751 \\ x-y=255 \end{gathered}$

If we add both of them together we get the following:

$\begin{gathered} x+y=751 \\ x-y=255 \\ -------- \\ 2x=1006 \\ \Rightarrow x=\frac{1006}{2}=503 \\ x=503 \end{gathered}$

now that we have the value of x, we can use it on any equation to find the value of y:

$\begin{gathered} 503+y=751 \\ \Rightarrow y=751-503=248 \\ y=248 \end{gathered}$

therefore, x = 503 and y = 248