bobby and zoe both attended a golf clinic with local golf pros. bobbys pro charged $120 plus $5 bucket of golf balls. zoes pro charged $80 plus $8 per bucket of golf balls. how many buckets of golf balls will zoe need need to purchase to spend at least the same amount of money as bobby?

We are asked to find how many buckets of golf balls Zoe needs to purchase in order to spend at least as much as Bobby.

### Step-by-Step Solution:

Let the number of buckets of golf balls be denoted by $ x $.

1. **Bobby's total cost**:  
   Bobby's pro charges $120 plus $5 per bucket of golf balls.
   \[
   \text{Bobby's total cost} = 120 + 5x
   \]
   
2. **Zoe's total cost**:  
   Zoe's pro charges $80 plus $8 per bucket of golf balls.
   \[
   \text{Zoe's total cost} = 80 + 8x
   \]
   
3. **Setting up the inequality**:  
   To find how many buckets Zoe needs to purchase to spend at least the same amount as Bobby, we set Zoe's total cost greater than or equal to Bobby's total cost:
   \[
   80 + 8x \geq 120 + 5x
   \]

4. **Solving the inequality**:  
   Subtract $ 5x $ from both sides:
   \[
   80 + 3x \geq 120
   \]
   Subtract 80 from both sides:
   \[
   3x \geq 40
   \]
   Divide by 3:
   \[
   x \geq \frac{40}{3} \approx 13.33
   \]
   
   Since the number of buckets must be a whole number, Zoe needs to purchase at least **14 buckets** of golf balls.

### Conclusion:
Zoe will need to purchase **14 buckets** of golf balls to spend at least as much as Bobby.

Do you want further details on any step or have additional questions?

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Here are some related questions:

1. How much will Zoe spend if she buys exactly 14 buckets of golf balls?
2. How much will Bobby spend if he buys 10 buckets of golf balls?
3. If both Zoe and Bobby buy 5 buckets, how much will each of them spend?
4. What is the difference in costs if Zoe buys 15 buckets and Bobby buys 12 buckets?
5. How would the scenario change if Bobby's pro increased the bucket price to $6 per bucket?

**Tip:** When solving inequalities, always check if rounding up is necessary for practical situations like counting objects.

Bobby and Zoe both attended a golf clinic with local golf pros. Bobby's pro charged $120 plus $5 per bucket of golf balls. Zoe's pro charged $80 plus $8 per bucket of golf balls. How many buckets of golf balls will Zoe need to purchase to spend at least the same amount of money as Bobby?

Explore how to solve a linear inequality to compare costs between Bobby and Zoe, where each pays different rates for golf lessons. Learn how many buckets of golf balls Zoe must buy to match Bobby's spending. Suitable for students in Grades 6-8.

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