Question

3. The numbers x and y satisfy the equations \( x(y+2)=100 \) and \( y(x+2)=60 \) What is the value of \( x-y \) A) 60 B) 50 C) 40 D) 30 E) 20

Ask by Huff Coles. in South Africa
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

\( x - y = 20 \), so the answer is E) 20.

Solution

1. Expand the first equation: \[ x(y+2)=xy+2x=100 \] 2. Expand the second equation: \[ y(x+2)=xy+2y=60 \] 3. Subtract the second equation from the first: \[ (xy+2x) - (xy+2y)=100-60 \] Simplify: \[ 2x-2y=40 \] 4. Divide both sides by 2: \[ x-y=20 \] Thus, the value of \( x-y \) is \( 20 \).

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Mind Expander

To find the value of \( x - y \), we start with the given equations: 1. \( x(y+2) = 100 \) 2. \( y(x+2) = 60 \) From the first equation, we can express \( y \) in terms of \( x \): \[ xy + 2x = 100 \implies xy = 100 - 2x \] From the second equation, we can express \( x \) in terms of \( y \): \[ yx + 2y = 60 \implies yx = 60 - 2y \] Since both expressions equal \( yx \), we can set them equal to each other: \[ 100 - 2x = 60 - 2y \] Rearranging gives: \[ 2y - 2x = 60 - 100 \] \[ 2y - 2x = -40 \implies y - x = -20 \implies x - y = 20 \] Thus, the value of \( x - y \) is \( \boxed{20} \).

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