A group of students decide to attend a concert. The cost of renting a bus to take them to the concert is $450, which is to be shared equally among the students. The concert promoters offer discounts to groups arriving by bus. Tickets normally costs $59 each but are reduced $0.10 per ticket for each person in the group (up to the maximum capacity of the bus). How many students must be in the group for the total cost per student to be less than $54?

Question

A group of students decide to attend a concert. The cost of renting a bus to take them to the concert is $450, which is to be shared equally among the students. The concert promoters offer discounts to groups arriving by bus. Tickets normally costs $59 each but are reduced $0.10 per ticket for each person in the group (up to the maximum capacity of the bus). How many students must be in the group for the total cost per student to be less than $54?

Answer 1

Is this correct?

but are reduced $0.10 per ticket for each person

Only 10 cents?

Answer 2

Yes. Only 10 cents. Keep in mind that it's not necessarily for one bus. Thanks.

Answer 3

To determine how many students must be in the group for the total cost per student to be less than $54, let's break down the problem step by step:

1. First, we need to calculate the total cost of tickets for the group. We know that the regular price of a ticket is $59, and there is a discount of $0.10 per ticket for each person in the group (up to the maximum capacity of the bus). Let's denote the number of students in the group as 'n'.

The discounted price per ticket is $59 - ($0.10 x n).

2. Now, we need to calculate the total cost per student, considering the rent cost of the bus as well. The total cost per student can be calculated by dividing the sum of the bus rent and the discounted ticket price by the number of students in the group.

Total cost per student = (Bus rent + Discounted ticket price) / n.

3. We want the total cost per student to be less than $54. So, we can set up the following inequality:

(Bus rent + Discounted ticket price) / n < $54.

4. Substitute the values we have into the inequality:

($450 + ($59 - ($0.10 x n))) / n < $54.

5. Simplify and solve the inequality for n:

($450 + $59 - $0.10n) / n < $54.

(509 - $0.10n) / n < $54.

509 - $0.10n < $54n.

509 < $54.10n.

509 < $540 + $0.10n.

509 - $540 < $0.10n.

-31 < $0.10n.

Divide both sides by 0.10:

-310 < n.

Therefore, we find that the number of students (n) must be greater than -310 for the total cost per student to be less than $54. Since the number of students cannot be negative, we can round up to the nearest whole number.

Hence, the minimum number of students required for the total cost per student to be less than $54 is 311.