Question

The sum of two numbers is 35. Their difference is 65.

Answer 1

We are given that the sum of two numbers is 35. If "x" and "y" are the numbers then this means mathematically the following:

$x+y=35,(1)$

Now we are told that this difference is 65, this can be expressed mathematically as:

$x-y=65,(2)$

Therefore, we have two equations and two variables. To solve this system we can add both equations together, in such a way that the variable "y" is eliminated, like this:

$x+y+x-y=35+65$

Solving the operations:

$2x=100$

Dividing both sides by 2:

$x=\frac{100}{2}=50$

The first number is 50. Now we replace this number in equation (1):

$50+y=35$

Subtracting 50 to both sides:

$\begin{gathered} y=35-50 \\ y=-15 \end{gathered}$

The numbers are 50 and -15.