A drama club is planning a bus trip to New York City to see a Broadway play. The cost per person for the bus rental varies inversely to the number of people going on the trip. It will cost $30 per person if 44 people go on the trip. How much will it cost per person if 20 people go on the trip? Round your answer to the nearest cent, if necessary.

Question

A drama club is planning a bus trip to New York City to see a Broadway play. The cost per person for the bus rental varies inversely to the number of people going on the trip. It will cost $30 per person if 44 people go on the trip. How much will it cost per person if 20 people go on the trip? Round your answer to the nearest cent, if necessary.

A. $44.00
B. $22.00
C. $33.50
D. $66.00

Answer 1

We know that the cost per person varies inversely with the number of people going on the trip, so we can set up an equation:

k = constant of proportionality
p = number of people
c = cost per person

k = cp

We're given that when 44 people go on the trip, the cost per person is $30:

30 = c(44)

Solving for c, we get:

c = 30/44

Now we can use this value of c to find the cost per person when 20 people go on the trip:

c = k/p
30/44 = k/20

Solving for k, we get:

k = (30/44) * 20
k = 13.64

Now we can use this value of k and the number of people going on the trip (20) to find the cost per person:

c = k/p
c = 13.64/20
c ≈ 0.682

Rounding to the nearest cent, we get:

c ≈ $0.68

So the answer is not one of the listed choices.

Answer 2

To solve this problem, we will use the concept of inverse variation. Inverse variation means that as one value increases, the other value decreases, and their product remains constant.

Let's denote the cost per person as "C" and the number of people as "N". According to the problem, we know that C and N are inversely proportional.

We can set up the equation using the formula for inverse variation: C × N = k, where k is a constant.

Given the information that it will cost $30 per person if 44 people go on the trip, we can substitute these values into our equation:

30 × 44 = k

Now we can solve for k:

k = 30 × 44 = 1320

So our equation becomes C × N = 1320.

To find out how much it will cost per person if 20 people go on the trip, we need to substitute 20 for N in our equation and solve for C:

C × 20 = 1320

Divide both sides by 20:

C = 1320 / 20 = 66

Therefore, it will cost $66.00 per person if 20 people go on the trip.

The answer is D. $66.00.

Answer 3

To solve this problem, we need to use the concept of inverse variation, which states that when two variables are inversely proportional, their product remains constant. In this case, the number of people going on the trip and the cost per person are inversely proportional.

We can set up a proportion to solve for the cost per person:

number of people / cost per person = constant

Let's apply this to the given information:

44 people / $30 per person = constant

To find the constant, we can solve for it:

constant = 44 * $30 = $1320

Now, we can use this constant value to find the cost per person when 20 people go on the trip:

20 people / cost per person = constant

20 / cost per person = $1320

Solving for cost per person:

cost per person = $1320 / 20

cost per person ≈ $66.00

Therefore, the cost per person if 20 people go on the trip is approximately $66.00.

So, the correct option is D. $66.00.