Joel needs 785 tickets to get the prize he wants at the arcade. He already has 284 tickets and can earn 35 tickets each time he plays an arcade game. How many games will he have to play to have enough tickets to win the prize he wants?

Joel must play at least 15 games to earn the remaining 501 tickets he needs for the prize at the arcade, after subtracting the 284 tickets he already has from the total 785 required.

Explanation:

Joel needs to accumulate a certain number of tickets to win a prize at the arcade. We can approach this problem by calculating the total number of tickets he still needs and then dividing that number by the amount of tickets he can earn per game.

Step-by-Step Calculation:

First, find out how many tickets Joel is short of the prize by subtracting the tickets he already has from the total number of tickets needed: 785 - 284.
Second, calculate how many games he needs to play by taking the remaining number of tickets and dividing it by the number of tickets he earns per game, which is 35.

Let's execute these steps:

Joel needs 785 tickets and has 284 tickets. So, the number of tickets he still needs is 785 - 284 = 501 tickets.
To find out how many games he needs to play, we divide the tickets he needs by tickets per game: 501 / 35. This gives us approximately 14.31, which means Joel needs to play at least 15 games to earn enough tickets, since he cannot play a fraction of a game.