Find Two Numbers by Sum and Ratio Calculator

Welcome to the free online calculator to find two numbers by sum and ratio. For example, the sum of two numbers is 80 and their ratio is 5:3. 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 = 80

Second equation: x:y = 5:3

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

x:y = 5:3

xy = 53

x = 5y3

Substitute this value into the first equation and solve.

x + y = 80

5y3 + y = 80

5y + 3y3 = 80

5y + 3y = 80 * 3

8y = 240

y = 2408

y = 30

y = 30, according to the relationship between x and y, we can calculate the value of x.

x = 5y3 = 5 * 303 = 50

So, the two numbers are 50 and 30.

Is it right or not? Check it out!

50 + 30 = 80

50:30 = 5:3

Yes, this is correct.

Another simple method, since the ratio between the two numbers is 5:3, then we can directly set these two numbers to 5a and 3a. The sum of them is 80. So, we can get the equation

5a + 3a = 80

8a = 80

a = 808

a = 10

Thus, the first number is 5a = 5 * 10 = 50, the second number is 3a = 3 * 10 = 30. The two numbers are also 50 and 30, same as the first method.

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