Question

The freshman class is putting on a variety show to raise money for their spring field trip. It cost $460 to rent the facility that they are going to use. If they charge $15 for each ticket, write an inequality to describe how many tickets they need to sell in order to raise at least $2000.

(I suck at word problems S-I-G-H)

Answer 1

No worries, let's break down the problem step by step.

To raise at least $2000, the amount they make from selling tickets (total revenue) must be greater than or equal to the sum of the rental cost and $2000:

Total revenue ≥ Rental cost + $2000

We know that the rental cost is $460, so we can substitute that in:

Total revenue ≥ $460 + $2000

Simplifying the right-hand side:

Total revenue ≥ $2460

Now we need to relate the total revenue to the number of tickets sold. We know that they charge $15 for each ticket, so the total revenue is equal to 15 times the number of tickets sold:

Total revenue = 15 x (number of tickets sold)

Substituting this into the inequality we derived earlier, we get:

15 x (number of tickets sold) ≥ $2460

Simplifying this inequality, we get:

number of tickets sold ≥ $2460 / $15

number of tickets sold ≥ 164

Therefore, the inequality to describe how many tickets they need to sell in order to raise at least $2000 is:

number of tickets sold ≥ 164

They need to sell at least 164 tickets to raise at least $2000, after paying the rental cost of $460.