Numbers Finder by Difference and Ratio
Input the difference and ratio of two numbers, and find the numbers instantly!
How to Calculate Two Numbers from Their Difference and Ratio
Given:
- \( D \): the difference between the two numbers, \( D = x - y \)
- \( R \): the ratio of 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 difference formula \( x - y = D \):
\( R \cdot y - y = D \)
\( y = \frac{D}{R - 1} \)
3. Find the first number (\( x \))
\( x = D + y \)
Examples
Example 1: Two numbers have a difference of 60 and a ratio of 5:4. Find the numbers.
Solution:
\( y = \frac{60}{ \frac{5}{4} - 1} = 240 \)
\( x = 60 + 240 = 300 \)
Result: The two numbers are 300 and 240.
Example 2: Two numbers have a difference of 115 and a ratio of 8:3. What are the numbers?
Solution:
\( y = \frac{115}{ \frac{8}{3} - 1} = 69 \)
\( x = 115 + 69 = 184 \)
Result: The two numbers are 184 and 69.