Find Two Numbers by Product and Ratio Calculator

Welcome to the free online calculator to find two numbers by product and ratio. For example, the product of two numbers is 360 and their ratio is 10:9. 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 = 360

Second equation:

x:y = 10:9

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

x:y = 10:9

xy = 109

x = 10y9

Substitute this value into the first equation and solve.

x * y = 360

10y9 * y = 360

10y² = 360 * 9

10y² = 3240

y² = 324

y = 18

y = 18, according to the relationship between x and y, we can calculate the value of x.

x = 10y9 = 10 * 189 = 20

So, the two numbers are 18 and 20.

Is it right or not? Check it out!

18 * 20 = 36

20:18 = 10:9

Yes, this is correct.

Another simple method, since the ratio between the two numbers is 10:9, then we can directly set these two numbers to 10a and 9a. The product of them is 360. So, we can get the equation

10a * 9a = 360

90a² = 360

a² = 4

a = 2

Thus, the first number is 10a = 10 * 2 = 20, the second number is 9a = 9 * 2 = 18. The two numbers are also 18 and 20, same as the first method.

The steps are simple but tedious, so we developed this calculator to find two numbers by product 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.