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?

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Answer 1 · 2015-10-14T00:12:21

#4" "# and #" "24#

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#