Question

Sam makes tote bags for a school fundraiser.

The fixed costs for making the bags is $30.
The cost of the materials for each bag is $8.50.
Sam can spend less than a total of $200 on the tote bags.
Write an inequality that can be used to determine
, the number of tote bags that can be made. Solve your inequality. Show your work.

Answer 1

To determine the number of tote bags that Sam can make while keeping costs under $200, we start by setting up the inequality.

**Fixed Costs:**
Sam has a fixed cost of $30 for making the bags.

**Variable Costs:**
The cost of materials for each bag is $8.50. If we let \( x \) represent the number of tote bags made, then the total cost for materials for \( x \) bags would be \( 8.50x \).

**Total Cost:**
The total cost for making \( x \) bags includes both fixed and variable costs, which can be expressed as:
\[
\text{Total Cost} = \text{Fixed Cost} + \text{Variable Cost} = 30 + 8.50x
\]

**Setting Up the Inequality:**
Since Sam wants to spend less than $200, we can write the inequality:
\[
30 + 8.50x < 200
\]

**Solving the Inequality:**
1. Subtract 30 from both sides:
\[
8.50x < 200 - 30
\]
\[
8.50x < 170
\]

2. Divide both sides by 8.50:
\[
x < \frac{170}{8.50}
\]

3. Calculate \( \frac{170}{8.50} \):
\[
\frac{170}{8.50} = 20
\]

Thus, the inequality simplifies to:
\[
x < 20
\]

**Conclusion:**
Sam can make a maximum of **19 tote bags** (since \( x \) has to be a whole number). Thus, \( x \) can take values \( 0, 1, 2, \ldots, 19 \).