Question

The cost of a college field trip is $378.24 for the cost of the bus plus $8.00 per student for lunch. If the school can afford to spend a maximum of $1620 on the trip, write and simplify an inequality that represents the number of students that can go on the trip. Represent your solution in at least 3 ways.

Answer 1

3 ways listed at bottom

Explanation:

The equation would be
`1620\geq 378.24+8s` (s for students)

Simplify:

`1620\geq 378.24+8s\\1620-378.24 \geq 8s\\1241.76\geq 8s\\155.22\geq s`

Way 1:
`s\leq 155.22`

Way 2: (-∞,155.22] OR [0,155.22] (2nd is OK {maybe})

Way 3:

Answer 2

The maximum is 155 students that can go on the field trip .

Explanation:

To find the number of students that can go on the trip, we need to write an inequality based on the given information.

Let's start by defining the variables:

Let 'x' be the number of students going on the trip.

According to the question, the cost of the bus is $378.24, and the cost per student for lunch is $8.00. The school can afford to spend a maximum of $1620 on the trip.

The cost of the bus is a fixed cost, so it remains the same regardless of the number of students. The cost of lunch, however, increases with the number of students.

The cost of the bus is $378.24, and the cost per student for lunch is $8.00. Therefore, the total cost of the trip can be represented by the equation:

Total cost = cost of the bus + (cost per student * number of students)

We know that the total cost of the trip should not exceed $1620. So, we can write the inequality as:

Total cost ≤ $1620

Substituting the values, we have:

$378.24 + ($8.00 * x) ≤ $1620

To simplify the inequality, we can perform the calculations:

$378.24 + $8.00x ≤ $1620

Now, let's solve the inequality:

$8.00x ≤ $1620 - $378.24

$8.00x ≤ $1241.76

To isolate 'x', we can divide both sides of the inequality by $8.00:

x ≤ $1241.76 / $8.00

Simplifying further:

x ≤ 155.22

Therefore, the number of students that can go on the trip is less than or equal to 155.22.

Since we can't have a fraction of a student, the number of students that can go on the trip should be a whole number. Thus, we can conclude that the maximum number of students that can go on the trip is 155.

In summary, the inequality representing the number of students that can go on the trip is:

x ≤ 155

Alternative ways to represent the solution:

1. The maximum number of students that can go on the trip is 155.

2. The number of students going on the trip must not exceed 155.

3. If there are more than 155 students, the school cannot afford the trip.