Question

Create a word problem for an algebra lesson on functions involving jars of tomato sauce stored in boxes.

Answer 1

**Word Problem:**

Maria is organizing her pantry and has a collection of jars of homemade tomato sauce. She decides to store the jars in boxes to keep everything neat and tidy.

In total, Maria has 48 jars of tomato sauce. She can fit exactly 6 jars into each box.

1. **Function Representation:**
- Let \( x \) represent the number of boxes Maria uses.
- Write a function \( f(x) \) that represents the total number of jars of tomato sauce stored in \( x \) boxes.

2. **Using the Function:**
- How many boxes will Maria need to store all 48 jars of tomato sauce?
- If Maria finds an additional 18 jars of tomato sauce, how many boxes will she need now?
- Write an equation to find out how many jars can she store if she uses \( x \) boxes.

**Questions:**
1. What is the function \( f(x) \)?
2. How many boxes are needed initially?
3. How many total jars does Maria have after finding the additional jars?
4. How many boxes will she need for her new total?

**Solution:**

1. The function \( f(x) \) can be defined as:
\[
f(x) = 6x
\]

2. To find how many boxes are needed for 48 jars:
\[
6x = 48 \implies x = \frac{48}{6} = 8
\]
So, Maria needs 8 boxes initially.

3. If she finds an additional 18 jars, her new total is:
\[
48 + 18 = 66 \text{ jars}
\]

4. To find how many boxes she will need for 66 jars:
\[
6x = 66 \implies x = \frac{66}{6} = 11
\]
Maria will need 11 boxes after finding the additional jars.