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

$4$ $4" "$ and $24$ $" "24$

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

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

$4 \cdot x + 8 = y$ $4 * x + 8 = y$

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

$4 x + y = 40$ $4x + y = 40$

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

Notice that if you substitute the value of $y$ $y$ 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 $" "y = 24$