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?

1 Answer
Oct 14, 2015

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