The difference between two positive integers is 63. The ratio of the two integers is 2:5. Find the two integers.

Question

Homi · Accepted Answer

We will use a common multiple to represent the integers and then form an equation.

Step 1 — Find the common multiple

Let's represent the two integers. We can use $2x$ and $5x$ for them. Their difference is given as 63. So, we can write an equation.

$5x - 2x = 63$

$3x = 63$

$x = \frac{63}{3}$

$\boxed{x = 21}$

Diagram 1

Step 2 — Calculate the integers

Now we will find the first integer. It is $2x$ .

$2x = 2 \times 21$

$= 42$

Let's find the second integer. It is $5x$ .

$5x = 5 \times 21$

$= 105$

The first integer is 42. The second integer is 105.

Question 4