Question
Solve for \( w \). \[ \frac{8}{5} w=40 \] Simplify your answer as much as possible. \[ w= \]
Ask by Elliott Newton. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( w = 25 \)
Solution
To solve for \( w \) in the equation:
\[
\frac{8}{5} w = 40
\]
Follow these steps:
1. **Isolate \( w \):**
Multiply both sides of the equation by the reciprocal of \(\frac{8}{5}\), which is \(\frac{5}{8}\):
\[
w = 40 \times \frac{5}{8}
\]
2. **Simplify the Multiplication:**
Divide 40 by 8:
\[
40 \div 8 = 5
\]
Then multiply by 5:
\[
5 \times 5 = 25
\]
3. **Final Solution:**
\[
w = 25
\]
**Answer:**
\[
w = 25
\]
Reviewed and approved by the UpStudy tutoring team
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Bonus Knowledge
To solve for \( w \), start by multiplying both sides of the equation by the reciprocal of \( \frac{8}{5} \), which is \( \frac{5}{8} \). This gives you: \[ w = 40 \times \frac{5}{8} \] Now, calculate \( 40 \times \frac{5}{8} \): \[ w = 40 \times 0.625 = 25 \] Thus, the simplified answer is: \[ w = 25 \]