# 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

#### Explanation:

Let's say that *smaller* number and *larger* number.

You know that if you multiply the smaller number by

#4 * x + 8 = y#

Moreover, you know that if you multiply the smaller number by

#4x + y = 40#

You now have a system of two equations with two unknowns,

Notice that if you substitute the value of

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

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

This means that

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

The two numbers are

#x = 4" "# and#" "y = 24#