Lucy plans to
spend between $50 and $65, inclusive, on
packages of beads and packages of charms. If
she buys 5 packages of beads at $4.95 each,
how many packages of charms at $6.55 can
Lucy buy while staying within her budget?

To solve this problem, we need to determine the number of packages of charms Lucy can buy while staying within her budget of $50 to $65, inclusive.

### Step-by-Step Solution

1. **Calculate the cost of the beads:**

   Lucy buys 5 packages of beads, each costing $4.95. The total cost for the beads is:

   \[
   \text{Cost of beads} = 5 \times 4.95 = 24.75
   \]

2. **Determine the remaining budget for charms:**

   Let $ x $ be the number of packages of charms that Lucy can buy, each costing $6.55. The cost for the charms is:

   \[
   \text{Cost of charms} = 6.55x
   \]

   The total cost of both beads and charms should be within her budget:

   \[
   50 \leq 24.75 + 6.55x \leq 65
   \]

3. **Solve the inequality:**

   - **Lower bound:**

     \[
     50 \leq 24.75 + 6.55x 
     \]

     Subtract 24.75 from both sides:

     \[
     50 - 24.75 \leq 6.55x 
     \]

     \[
     25.25 \leq 6.55x 
     \]

     Divide by 6.55:

     \[
     \frac{25.25}{6.55} \leq x 
     \]

     \[
     3.8557 \leq x 
     \]

   - **Upper bound:**

     \[
     24.75 + 6.55x \leq 65
     \]

     Subtract 24.75 from both sides:

     \[
     6.55x \leq 65 - 24.75 
     \]

     \[
     6.55x \leq 40.25 
     \]

     Divide by 6.55:

     \[
     x \leq \frac{40.25}{6.55}
     \]

     \[
     x \leq 6.140
     \]

4. **Determine the possible values for $ x $:**

   Since $ x $ must be a whole number, the possible values for $ x $ are:

   \[
   x = 4, 5, \text{or} 6
   \]

   Lucy can buy 4, 5, or 6 packages of charms to stay within her budget.

### Conclusion

Lucy can buy **4, 5, or 6 packages** of charms while staying within her budget of $50 to $65.

---

Would you like more details, or do you have any questions?

### Related Questions

1. What if the cost of the beads changes to $5.50 per package? How does this affect the number of charm packages Lucy can buy?
2. How many total packages (beads and charms combined) can Lucy buy while staying within a $100 budget?
3. What is the maximum number of packages Lucy can buy if charms are on a 10% discount?
4. If Lucy decides to spend at least $55, how many packages of charms must she buy?
5. How much would Lucy spend if she bought 3 packages of beads and 4 packages of charms?

**Tip:** When solving inequalities involving multiple steps, always carefully isolate the variable by performing inverse operations systematically.

Lucy plans to spend between $50 and $65, inclusive, on packages of beads and packages of charms. If she buys 5 packages of beads at $4.95 each, how many packages of charms at $6.55 can Lucy buy while staying within her budget?

Learn how to solve a budgeting problem where Lucy buys beads and charms while staying within a budget of $50 to $65. This problem involves algebraic inequalities and linear equations to find the maximum number of charm packages Lucy can afford. Suitable for students in Grades 7-9.

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