Question

What are two numbers with a sum of 35 and a difference of 7?

Answer 1

Make a system of equations using the given information and solve to find the numbers are `21` and `14`.

Explanation:

The first thing to do in algebraic equations is to assign variables to what you don't know. In this case, we don't know either number so we'll call them `x` and `y`.

The problem gives us two key bits of info. One, these numbers have a difference of `7`; so when you subtract them, you get `7`:
`x-y=7`

Also, they have a sum of `35`; so when you add them, you get `35`:
`x+y=35`

We now have a system of two equations with two unknowns:
`x-y=7`
`x+y=35`

If we add them together, we see we can cancel the `y`s:
`color(white)(X)x-y=7`
`+ul(x+y=35)`
`color(white)(X)2x+0y=42`
`->2x=42`

Now divide by `2` and we have `x=21`. From the equation `x+y=35`, we can see that `y=35-x`. Using this and the fact that `x=21`, we can solve for `y`:
`y=35-x`
`->y=35-21=14`

So the two numbers are `21` and `14`, which do indeed add to `35` and have a difference of `7`.