Question

The difference between two positive integers is $75$. The ratio of these integers is $7:4$. Find the integers.

Answer 1

Let the two integers be $x$ and $y$

$\Rightarrow x-y=75$

$\frac{x}{y}=\frac{7}{4}$

$\Rightarrow 4x=7y$

$\Rightarrow x=\frac{7y}{4}$

$\Rightarrow \frac{7y}{4}-y=75$

$\Rightarrow \frac{3y}{4}=75$

$\Rightarrow y=100$

$\Rightarrow x=175$.