The table below gives information about the meals chosen by 45 people in a restaurant.

\begin{tabular}{|c|c|c|c|c|}
\cline { 2 - 5 } \multicolumn{1}{c|}{} & Salad & Pasta & Pizza & Total \\
\hline Fruit & 6 & 3 & & 12 \\
\hline Yogurt & & & 5 & \\
\hline Ice cream & 1 & 4 & & \\
\hline Total & 10 & & 22 & \\
\hline
\end{tabular}

a) Complete the table.

b) How many people had pizza?

c) How many people chose salad or fruit?

[tex]$\square$[/tex]



Answer :

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]