Esteben and his family are making care packages to send to children at summer camp. Each complete car package contains 5 pens, 2 notebooks, 3 envelopes, 12 cookies, and 5 candy bars. Esteban and his family have already made 7 complete care packages and the following materials remain:
3 boxes of pens (10 pens per box)
4 boxes of notebooks (5 notebooks per box)
2 boxes of envelopes (12 envolopes per box)
84 cookies
`4 1/2` boxes of candy bars (10 candy bars per box)
How many additional complete care packages can Esteban and his family make with the remaining materials?

Options

A. `6`
B. `7`
C. `8`
D. `10`

Answer

To determine how many additional complete care packages Esteban and his family can make with the remaining materials, we will follow these steps:

### Step 1: Calculate the total remaining materials
1. **Pens**: 3 boxes of pens with 10 pens each.
\[ 3 \text{ boxes} \times 10 \text{ pens/box} = 30 \text{ pens} \]

2. **Notebooks**: 4 boxes of notebooks with 5 notebooks each.
\[ 4 \text{ boxes} \times 5 \text{ notebooks/box} = 20 \text{ notebooks} \]

3. **Envelopes**: 2 boxes of envelopes with 12 envelopes each.
\[ 2 \text{ boxes} \times 12 \text{ envelopes/box} = 24 \text{ envelopes} \]

4. **Cookies**: 84 cookies remain.

5. **Candy Bars**: 4.5 boxes of candy bars with 10 candy bars each.
\[ 4.5 \text{ boxes} \times 10 \text{ candy bars/box} = 45 \text{ candy bars} \]

### Step 2: Determine how many complete care packages can be made from each material
Each complete care package requires:
- 5 pens
- 2 notebooks
- 3 envelopes
- 12 cookies
- 5 candy bars

Now we will calculate how many packages can be made from each material:

1. **Pens**:
\[ \frac{30 \text{ pens}}{5 \text{ pens/package}} = 6 \text{ packages} \]

2. **Notebooks**:
\[ \frac{20 \text{ notebooks}}{2 \text{ notebooks/package}} = 10 \text{ packages} \]

3. **Envelopes**:
\[ \frac{24 \text{ envelopes}}{3 \text{ envelopes/package}} = 8 \text{ packages} \]

4. **Cookies**:
\[ \frac{84 \text{ cookies}}{12 \text{ cookies/package}} = 7 \text{ packages} \]

5. **Candy Bars**:
\[ \frac{45 \text{ candy bars}}{5 \text{ candy bars/package}} = 9 \text{ packages} \]

### Step 3: Identify the limiting factor
The number of complete packages that can be made is determined by the material that allows for the least number of packages. From our calculations:
- Pens: 6 packages
- Notebooks: 10 packages
- Envelopes: 8 packages
- Cookies: 7 packages
- Candy Bars: 9 packages

The limiting factor is **pens**, which allows for only **6 complete care packages**.

### Step 4: Conclusion
Esteban and his family can make **6 additional complete care packages** with the remaining materials.

---