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 Question from Patrick: The difference of two numbers is 42 and the larger number is 8/5 of the smaller number. Find the two numbers.

Hi Patrick,

I am going to solve a similar problem.

The difference of two numbers is 3 and the larger number is 5/4 of the smaller number. Find the two numbers.

Suppose the two numbers are $x$ and $y,$ where $y$ is the larger. Since the difference is 3 you know that

$y - x = 3.$

Since the larger number is 5/4 of the smaller you also know that

$y = \frac{5}{4} \times x.$

Substitute this equation into the first equation to get

$\frac{5}{4} x - x = 3.$

Thus

$\frac{1}{4} x = 3 \mbox{ or } x = 12.$

The larger number is 3 more than 12 so $y = 15.$