Sure, let's complete the problem step-by-step based on the table provided.
a) Complete the table
To start, we need to fill in the missing values in the table. Here are the given values:
| | Salad | Pasta | Pizza | Total |
|--------------|-------|-------|-------|-------|
| Fruit | 6 | 3 | ? | 12 |
| Yogurt | ? | ? | 5 | ? |
| Ice cream| 1 | 4 | ? | ? |
| Total | 10 | ? | 22 | 45 |
1. Calculate missing value for Fruit (Pizza):
- Total number of fruit meals = 12
- Number of fruit salads = 6
- Number of fruit pastas = 3
[tex]\[
\text{Fruit Pizza} = 12 - 6 - 3 = 3
\][/tex]
2. Calculate total Pasta:
- Total number of people (45)
- Number of people who had fruit (12)
- Number of people who had yogurt (calculated as shown below)
- Number of people who had ice cream (calculated as shown below)
- Number of salads (10)
- Number of pizza meals (22)
[tex]\[
\text{Missing Pasta} = 45 - (12 + Yogurt Total + Ice Cream Total)
\][/tex]
3. Calculate Yogurt values:
- Total number of pizza eaters = 22
- Number of fruit pizza = 3
- Remaining pizza (primarily yogurt and ice cream)
[tex]\[
\text{Yogurt Pizza} = 5
\][/tex]
[tex]\[
\text{Total Yogurt} = \text{Pizza Total} - \text{Fruit Pizza}
\][/tex]
[tex]\[
Yogurt Total = 22 - 3 = 19
\][/tex]
4. Calculate Ice Cream values:
- Total number of people = 45
- Total number of fruit meals = 12
- Total number of yogurt meals = Yogurt Total calculated above
[tex]\[
\text{Ice Cream Total} = 45 - 12 - 19 = 14
\][/tex]
5. Calculate Ice Cream Pizza:
- Total pizzas = 22
- Number of fruit pizza = 3
- Number of yogurt pizza = 5
[tex]\[
\text{Ice Cream Pizza} = 22 - 3 - 5 = 14
\][/tex]
6. Calculate total Pasta:
- Ice Cream Pasta already provided = 4
- Fruit Pasta = 3
[tex]\[
\text{Total Pasta} = 3 + 4 = 7
\][/tex]
7. Calculate Yogurt Pasta:
- Total number of people = 45
- Subtracting all known quantities:
[tex]\[
\text{Yogurt Pasta} = 45 - (6 + 3 + 3 + 5 + 1 + 4 + 14)
\][/tex]
[tex]\[
Yogurt Pasta = 45 - 36 = 9
\][/tex]
Our completed table looks like this:
| | Salad | Pasta | Pizza | Total |
|--------------|-------|-------|-------|-------|
| Fruit | 6 | 3 | 3 | 12 |
| Yogurt | 9 | 9 | 5 | 19 |
| Ice cream| 1 | 4 | 14 | 14 |
| Total | 10 | 7 | 22 | 45 |
b) How many people had pizza?
The total number of people who had pizza is provided directly in the table.
[tex]\[
\text{Number of people who had pizza} = 22
\][/tex]
c) How many people chose salad or fruit?
1. Total number of salads:
[tex]\[
\text{Total Salad} = 10
\][/tex]
2. Total number of fruit meals:
[tex]\[
\text{Total Fruit} = 12
\][/tex]
3. Combined (since there's no double counting mentioned, we assume separate categories):
[tex]\[
\text{Salad or Fruit} = 10 + 12 = 22
\][/tex]
So, summing up:
[tex]\[
\text{Number of people who had pizza} = 22
\][/tex]
[tex]\[
\text{Number of people who chose salad or fruit} = 22
\][/tex]
