Question
If \( x+y=25 \) \( x-y=5 \) What is Value of \( \frac{x}{3} \) W
Ask by Moreno Gibbs. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(\frac{x}{3} = 5\)
Solution
1. Given the equations:
- \( x + y = 25 \)
- \( x - y = 5 \)
2. Add the two equations to eliminate \( y \):
\[
(x+y) + (x-y) = 25 + 5
\]
\[
2x = 30
\]
\[
x = \frac{30}{2} = 15
\]
3. Now, compute \(\frac{x}{3}\):
\[
\frac{x}{3} = \frac{15}{3} = 5
\]
Thus, the value of \(\frac{x}{3}\) is \( 5 \).
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Simplify this solution Bonus Knowledge
To solve the system of equations given by \( x + y = 25 \) and \( x - y = 5 \), we can add these two equations together. Adding them: \[ (x+y) + (x-y) = 25 + 5 \] This simplifies to: \[ 2x = 30 \] Dividing both sides by 2 gives us: \[ x = 15 \] Now, substitute \( x = 15 \) back into the first equation to find \( y \): \[ 15 + y = 25 \implies y = 10 \] Now that we have \( x \), we can find \( \frac{x}{3} \): \[ \frac{x}{3} = \frac{15}{3} = 5 \] So, the value of \( \frac{x}{3} \) is \( 5 \).
