Question

A museum charges $30 for parking, plus $18 per person.

Make a table to show how much it will cost for a car to come with 1, 2, and 3 people.



Number of People Cost
1
44

2
66

3
84



(b)
Is this relationship proportional?

A
Yes

B
No

(c)
If you answered Yes for b, what is the constant of proportionality? If you answered No for b, explain how the museum could make an adjustment to their ticket policy to make it proportional.

Copy
Cut
Paste

Answer 1

Let's start by filling out the table with the correct costs for 1, 2, and 3 people:

The fixed parking fee is $30, and each person is charged $18.

**Cost Calculation:**
- For 1 person: \(30 + (1 \times 18) = 30 + 18 = 48\)
- For 2 people: \(30 + (2 \times 18) = 30 + 36 = 66\)
- For 3 people: \(30 + (3 \times 18) = 30 + 54 = 84\)

Now, let's complete the table:

| Number of People | Cost |
|------------------|------|
| 1 | 48 |
| 2 | 66 |
| 3 | 84 |

(b) Is this relationship proportional?

### Answer:
B. No

### Explanation:
A relationship is proportional if it can be represented as \(y = kx\), where \(k\) is the constant of proportionality. In this case, the cost does not increase consistently per person, because of the fixed parking fee. Instead, the cost has an initial fee of $30 that does not vary with the number of people.

(c) To make it proportional, the museum could adjust their ticket policy by eliminating the fixed parking fee and charging only based on the number of people. For example, they could charge $18 per person only without the $30 parking fee. Then the relationship would be directly proportional, represented as:

**New Cost Calculation for Proportionality Example:**
- For 1 person: \(1 \times 18 = 18\)
- For 2 people: \(2 \times 18 = 36\)
- For 3 people: \(3 \times 18 = 54\)

In this scenario, the total cost would directly correlate with the number of people, creating a proportional relationship.