1. Let \( x \) be the number of times Sara withdraws $60.
- Initial amount: $950
- Amount withdrawn: \( 60x \)
- Remaining amount: \( 950 - 60x \)
- She wants to have at least $600 left: \( 950 - 60x \geq 600 \)
- Solve for \( x \):
\[
950 - 60x \geq 600 \\
-60x \geq -350 \\
x \leq \frac{350}{60} \\
x \leq 5.83
\]
- Since \( x \) must be a whole number, the maximum is 5.
- Answer: Sara can withdraw money 5 times.
2. Let \( m \) be the number of miles traveled.
- Base cost: $70
- Cost per mile: $0.15
- Total cost: \( 70 + 0.15m \)
- Budget constraint: \( 70 + 0.15m \leq 100 \)
- Solve for \( m \):
\[
0.15m \leq 30 \\
m \leq \frac{30}{0.15} \\
m \leq 200
\]
- Answer: You can travel up to 200 miles.
3. Let \( x \) be the score on the last test.
- Current scores: 81, 89, 90, 78
- Average needed: at least 85
- Inequality: \( \frac{81 + 89 + 90 + 78 + x}{5} \geq 85 \)
- Simplify numerator: \( \frac{338 + x}{5} \geq 85 \)
- Multiply both sides by 5: \( 338 + x \geq 425 \)
- Solve for \( x \): \( x \geq 87 \)
- Answer: Jessica needs at least an 87 on her last test.
Parent Tip: Review the logic above to help your child master the concept of inequalities word problems worksheet pdf.
