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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Simplify this solution 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 \( \boxed{20} \).
