Question

One number is 20 more than another. If the the greater number is increased by 4, the result is five times the smaller. Find the two numbers

Answer 1

Let's translate the sentences into equations:

One number is 20 more than another: $x=20+y$

If the greater number is increased by 4: $x+4\ldots$

The result is five times the smaller [/tex]\ldots=5y[/tex]

So, we have the following system:

$\begin{cases}x=20y\\x+4=5y\end{cases}$

Use the expression for x given by the first equation to solve the second:

$x+4=5y \iff 20+y+4 = 5y \iff 24= 4y \iff y = 6$

which easily implies

$x=y+20 = 26$