Question

The larger of two numbers is 8 more than four times the smaller. If the larger is increased by four times the smaller, the result is 40. What are the numbers?

Answer 1

`4" "` and `" "24`

Explanation:

Let's say that `x` is the smaller number and `y` is the larger number.

You know that if you multiply the smaller number by `4` and add `8`, you get the larger number. This means that you can write

`4 * x + 8 = y`

Moreover, you know that if you multiply the smaller number by `4` and add it to the larger number, the result will be `40`.

`4x + y = 40`

You now have a system of two equations with two unknowns, `x` and `y`.

Notice that if you substitute the value of `y` from the first equation into the second equation, you get

`4x + underbrace(4x + 8)_(color(blue)(=y)) = 40`

`8x = 32 implies x = 32/8 = color(green)(4)`

This means that `y` is

`y = 4 * (color(green)(4)) + 8 = color(green)(24)`

The two numbers are

`x = 4" "` and `" "y = 24`