To complete the table, we'll first reveal the consistent ratio we have between the number of pizzas and the number of students based on the provided data.
Given the relationships:
- 2 pizzas feed 9 students.
- 10 pizzas feed 45 students.
- 100 pizzas feed 450 students.
From these, we can observe that if 10 pizzas feed 45 students, then 1 pizza feeds [tex]\( \dfrac{45}{10} = 4.5 \)[/tex] students. Using this ratio, we can calculate the number of pizzas required for the varying number of students.
Now, let's complete the provided table regarding the number of pizzas for given students:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
Pizzas & 2 & 10 & 100 & 30 & 60 & 50 & 200 & 300 \\
\hline
Students & 9 & 45 & 450 & 135 & 270 & 225 & 900 & 1350 \\
\hline
\end{tabular}
\][/tex]
### Explanation of calculations for each missing value:
- 135 students:
Using the ratio [tex]\( 1 \text{ pizza} : 4.5 \text{ students} \)[/tex], we calculate:
[tex]\[
\text{Pizzas} = \frac{135}{4.5} = 30
\][/tex]
- 270 students:
Using the ratio [tex]\( 1 \text{ pizza} : 4.5 \text{ students} \)[/tex], we calculate:
[tex]\[
\text{Pizzas} = \frac{270}{4.5} = 60
\][/tex]
- 225 students:
Using the ratio [tex]\( 1 \text{ pizza} : 4.5 \text{ students} \)[/tex], we calculate:
[tex]\[
\text{Pizzas} = \frac{225}{4.5} = 50
\][/tex]
- 900 students:
Using the ratio [tex]\( 1 \text{ pizza} : 4.5 \text{ students} \)[/tex], we calculate:
[tex]\[
\text{Pizzas} = \frac{900}{4.5} = 200
\][/tex]
- 1350 students:
Using the ratio [tex]\( 1 \text{ pizza} : 4.5 \text{ students} \)[/tex], we calculate:
[tex]\[
\text{Pizzas} = \frac{1350}{4.5} = 300
\][/tex]
### Solution to Additional Questions:
(a) How many students will 12 pizzas feed?
Since 1 pizza feeds 4.5 students, we calculate:
[tex]\[
\text{Students} = 12 \times 4.5 = 54
\][/tex]
So, 12 pizzas will feed 54 students.
(b) How many students will 20 pizzas feed?
Using the same ratio, we find:
[tex]\[
\text{Students} = 20 \times 4.5 = 90
\][/tex]
Thus, 20 pizzas will feed 90 students.
(c) How many students will 90 pizzas feed?
Similarly:
[tex]\[
\text{Students} = 90 \times 4.5 = 405
\][/tex]
Therefore, 90 pizzas will feed 405 students.
By maintaining a constant ratio, we can derive all necessary values accurately.
