Find Two Numbers by Difference and Ratio Calculator

Welcome to the free online calculator to find two numbers by difference and ratio. For example, the difference of two numbers is 115 and their ratio is 8:3. What are the numbers?

In the above example, assuming the two numbers are x and y.

Now, we can list the two equations based on the problem description.

First equation:

x – y = 115

Second equation:

x:y = 8:3

Simplify the second equation, let x be represented by y.

x:y = 8:3

xy = 83

x = 8y3

Substitute this value into the first equation and solve.

x – y = 115

8y3 – y = 115

8y – 3y3 = 115

8y – 3y = 115 * 3

5y = 345

y = 3455

y = 69

y = 69, according to the relationship between x and y, we can calculate the value of x.

x = 8y3 = 8 * 693 = 184

So, the two numbers are 184 and 69.

Is it right or not? Check it out!

184 – 69 = 115

184:69 = 8:3

Yes, this is correct.

Another simple method, since the ratio between the two numbers is 8:3, then we can directly set these two numbers to 8a and 3a. The difference of them is 115. So, we can get the equation

8a – 3a = 115

5a = 115

a = 1155

a = 23

Thus, the first number is 8a = 8 * 23 = 184, the second number is 3a = 3 * 23 = 69. The two numbers are also 184 and 69, same as the first method.

The steps are simple but tedious, so we developed this calculator to find two numbers by difference and ratio. The calculator simplifies all the steps above and gets the answer in milliseconds.

Next, we will introduce how to use the calculator.

Using the calculator is simple, follow these 3 steps:

Next, let’s look at some examples.