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`