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Sagot :
Certainly! Let's work through this problem step-by-step.
### Step 1: Determine the Number of Pizzas Needed
First, we need to calculate the number of pizzas required to serve 30 students, where each pizza serves 8 students.
Using the formula:
[tex]\[ \text{Number of pizzas needed} = \left\lceil \frac{\text{Number of students}}{\text{Servings per pizza}} \right\rceil \][/tex]
Plugging in the values:
[tex]\[ \text{Number of pizzas needed} = \left\lceil \frac{30}{8} \right\rceil \][/tex]
30 divided by 8 is 3.75. Since we cannot have a fraction of a pizza, we round up to the next whole number, which is 4. Therefore, 4 pizzas are needed to serve 30 students.
### Step 2: Calculate the Total Amount of Pizza Sauce Needed
Next, we need to determine how much pizza sauce is required for 4 pizzas. According to the recipe, one pizza requires [tex]\(\frac{2}{3}\)[/tex] cup of sauce. We need to multiply this by the number of pizzas.
[tex]\[ \text{Total amount of sauce for 4 pizzas} = 4 \times \frac{2}{3} \][/tex]
Carrying out the multiplication:
[tex]\[ 4 \times \frac{2}{3} = \frac{8}{3} = 2.\overline{6} \][/tex]
So, the total amount of pizza sauce needed is approximately 2.67 cups.
### Step 3: Determine the Sauce Required for Multiple Pizzas
Now, we need to fill out the pizza sauce amounts for 2, 3, and 4 pizzas as indicated in the provided table.
- For 2 pizzas:
[tex]\[ \text{Sauce for 2 pizzas} = 2 \times \frac{2}{3} = \frac{4}{3} = 1.\overline{3} \][/tex]
- For 3 pizzas:
[tex]\[ \text{Sauce for 3 pizzas} = 3 \times \frac{2}{3} = \frac{6}{3} = 2 \][/tex]
- For 4 pizzas:
[tex]\[ \text{Sauce for 4 pizzas} = 4 \times \frac{2}{3} = \frac{8}{3} = 2.\overline{6} \][/tex]
### Step 4: Complete the Table
We can now fill in the recipe table:
[tex]\[ \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{Pizza Sauce Recipe} \\ \hline Pizzas & Pizza Sauce \\ \hline 1 & $\frac{2}{3}$ cup \\ \hline 2 & $1.\overline{3}$ cups \\ \hline 3 & 2 cups \\ \hline 4 & $2.\overline{6}$ cups \\ \hline \end{tabular} \][/tex]
### Summary:
- Number of pizzas needed: 4
- Total amount of sauce needed: 2.\overline{6} cups
- Sauce for 2 pizzas: 1.\overline{3} cups
- Sauce for 3 pizzas: 2 cups
- Sauce for 4 pizzas: 2.\overline{6} cups
### Step 1: Determine the Number of Pizzas Needed
First, we need to calculate the number of pizzas required to serve 30 students, where each pizza serves 8 students.
Using the formula:
[tex]\[ \text{Number of pizzas needed} = \left\lceil \frac{\text{Number of students}}{\text{Servings per pizza}} \right\rceil \][/tex]
Plugging in the values:
[tex]\[ \text{Number of pizzas needed} = \left\lceil \frac{30}{8} \right\rceil \][/tex]
30 divided by 8 is 3.75. Since we cannot have a fraction of a pizza, we round up to the next whole number, which is 4. Therefore, 4 pizzas are needed to serve 30 students.
### Step 2: Calculate the Total Amount of Pizza Sauce Needed
Next, we need to determine how much pizza sauce is required for 4 pizzas. According to the recipe, one pizza requires [tex]\(\frac{2}{3}\)[/tex] cup of sauce. We need to multiply this by the number of pizzas.
[tex]\[ \text{Total amount of sauce for 4 pizzas} = 4 \times \frac{2}{3} \][/tex]
Carrying out the multiplication:
[tex]\[ 4 \times \frac{2}{3} = \frac{8}{3} = 2.\overline{6} \][/tex]
So, the total amount of pizza sauce needed is approximately 2.67 cups.
### Step 3: Determine the Sauce Required for Multiple Pizzas
Now, we need to fill out the pizza sauce amounts for 2, 3, and 4 pizzas as indicated in the provided table.
- For 2 pizzas:
[tex]\[ \text{Sauce for 2 pizzas} = 2 \times \frac{2}{3} = \frac{4}{3} = 1.\overline{3} \][/tex]
- For 3 pizzas:
[tex]\[ \text{Sauce for 3 pizzas} = 3 \times \frac{2}{3} = \frac{6}{3} = 2 \][/tex]
- For 4 pizzas:
[tex]\[ \text{Sauce for 4 pizzas} = 4 \times \frac{2}{3} = \frac{8}{3} = 2.\overline{6} \][/tex]
### Step 4: Complete the Table
We can now fill in the recipe table:
[tex]\[ \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{Pizza Sauce Recipe} \\ \hline Pizzas & Pizza Sauce \\ \hline 1 & $\frac{2}{3}$ cup \\ \hline 2 & $1.\overline{3}$ cups \\ \hline 3 & 2 cups \\ \hline 4 & $2.\overline{6}$ cups \\ \hline \end{tabular} \][/tex]
### Summary:
- Number of pizzas needed: 4
- Total amount of sauce needed: 2.\overline{6} cups
- Sauce for 2 pizzas: 1.\overline{3} cups
- Sauce for 3 pizzas: 2 cups
- Sauce for 4 pizzas: 2.\overline{6} cups
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