Numbers Finder by Sum and Ratio

Input the sum and ratio of two numbers, and find the numbers effortlessly!

Calculate Two Numbers from Their Sum and Ratio

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Result

How to Calculate Two Numbers from Their Sum and Ratio

Given:

  • \( S \): the sum of the two numbers, \( S = x + y \)
  • \( R \): the ratio between the two numbers, \( R = x : y \)

Steps to calculate:

1. Set the ratio

If \( R = x : y \), then \( x = R \cdot y \).

2. Find the second number (\( y \))

Substitute into the sum equation \( x + y = S \):

\( R \cdot y + y = S \)

\( y = \frac{S}{R + 1} \)

3. Find the first number (\( x \))

\( x = S - y \)

Examples

Example 1: Two numbers have a sum of 405 and a ratio of 7:8. Find the numbers.

Solution:

\( y = \frac{405}{\frac{7}{8} + 1} = 216 \)

\( x = 405 - 216 = 189 \)

Result: The two numbers are 189 and 216.

Example 2: Two numbers have a sum of 360 and a ratio of 3:5. What are the numbers?

Solution:

\( y = \frac{360}{\frac{3}{5} + 1} = 225 \)

\( x = 360 - 225 = 135 \)

Result: The two numbers are 135 and 225.

Example 3: Two numbers have a sum of 775 and a ratio of 14:17. Find the numbers.

Solution:

\( y = \frac{775}{\frac{14}{17} + 1} = 425 \)

\( x = 775 - 425 = 350 \)

Result: The two numbers are 350 and 425.