Numbers Finder by Difference and Quotient

Input the difference and quotient of two numbers, and find their exact values instantly!

Calculate Two Numbers Using Their Difference and Quotient

Result

How to Calculate Two Numbers Using Their Difference and Quotient

Given:

\( D \): the difference between the two numbers (\( x - y \))
\( Q \): the quotient of the two numbers (\( \frac{x}{y} \))

Steps:

Set up relationships: \( x - y = D, \quad \frac{x}{y} = Q \)
Express \( x \) in terms of \( y \): \( x = Q \cdot y \)
Substitute into the difference equation: \( Q \cdot y - y = D \)
Factorize \( y \): \( (Q - 1) \cdot y = D \)
Solve for \( y \): \( y = \frac{D}{Q - 1} \)
Find \( x \): \( x = y + D \)

Examples

Example 1: The difference between two numbers is 18, and their quotient is 10. What are the numbers?

Solution:

1. Solve for \( y \):

\( y = \frac{18}{10 - 1} = \frac{18}{9} = 2 \)

2. Calculate \( x \):

\( x = 2 + 18 = 20 \)

Result: The numbers are 20 and 2.

Example 2: The difference between two numbers is 75, and their quotient is 4. What are the numbers?

Solution:

1. Solve for \( y \):

\( y = \frac{75}{4 - 1} = \frac{75}{3} = 25 \)

2. Calculate \( x \):

\( x = 25 + 75 = 100 \)

Result: The numbers are 100 and 25.

Example 3: The difference between two numbers is 90, and their quotient is 10. What are the numbers?

Solution:

1. Solve for \( y \):

\( y = \frac{90}{10 - 1} = \frac{90}{9} = 10 \)

2. Calculate \( x \):

\( x = 10 + 90 = 100 \)

Result: The numbers are 100 and 10.