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=(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.