I paid $2480 for the facility and also need to pay $14 for each person who participates. I am charging each participant $54, how many people must compete to break even

62 people must compete to break even.

Step-by-step explanation:

The money paid for the facility is $2480. $14 is paid for each participant and each person that participate in the competition is charged $54.

In order to break even(profit is same as cost), the amount of money spent(cost) must be equal to the money gotten(revenue).

Let us assume that x number of people participated, therefore $14x would be spent for x number of people. The total cost would the be $(14x + 2480)

Also the money to be charged for x people would be $54x.

At break even, total cost = total money gained(revenue)

⇒ 2480 + 14x = 54x

2480 + 14x - 14x = 54x - 14x

∴ 30x = 2480

40x/40 = 2480/40

x = 62

Therefore 62 people must compete to break even.

the solution, from the graphing of the two lines, is (3,2), i.e., x = 3, y = 2.