# What are two numbers such that the greater number is 75% more than the lesser number?

May 2, 2018

Any two numbers of the form $x \mathmr{and} \frac{7}{4} x$. If we limit them to be natural numbers, the smallest solution is $4 \mathmr{and} 7.$

#### Explanation:

Let the lesser number be $x .$
The greater number is 75% more than $x$. So, it must be:
$= x + \left(\frac{75}{100}\right) x$
$= x + \frac{3}{4} x$
$= \frac{7}{4} x$

Thus the answer is any two numbers of the form$\left(x , \frac{7}{4} x\right) .$ Setting $x = 4$ makes both a natural number. So, the smallest answer(if $x \in N$) is $\left(4 , 7\right)$.

May 2, 2018

$x = 1 , y = 1.75$
$x = 2 , y = 3.5$
$x = 4 , y = 7$

These are examples, there are an infinite set of numbers you can use.

#### Explanation:

Let's call y the larger number, and x the lesser.

$y = 1.75 x$

From here you can insert any number x, and get a y value that satisfies your problem.

Examples:
$x = 1 , y = 1.75$
$x = 2 , y = 3.5$
$x = 4 , y = 7$