Question

Enzo and Beatriz are playing games at the local arcade. Incredibly Enzo wins five tickets from every game and Beatriz wins 11 tickets from every game. When they stopped playing games, Angelo Enzo and Beatrice had won the same number of total tickets. What is the minimum of games that Enzo could have played?

Answer 1

The smallest common multiple of the number of tickets won per game by Enzo (5) and Beatriz (11) is 55 tickets. Therefore, Enzo must have played a minimum of 11 games to have the same number of total tickets as Beatriz.

Step-by-step explanation:

To find the minimum number of games Enzo could have played for both to have the same number of tickets, we need to find the smallest common multiple of the number of tickets they win per game.

Since Enzo wins 5 tickets per game and Beatriz wins 11 tickets per game, we are looking for the smallest number that is both a multiple of 5 and 11.

To solve this, we can list the multiples of 5 (5, 10, 15, 20...) and 11 (11, 22, 33, 44...) until we find the smallest common multiple.

In this case, since 11 is a prime number and doesn't share any factors with 5, their first common multiple is simply the product of 5 and 11, which is 55 tickets.

Therefore, Enzo needs to play 55 / 5 = 11 games to have the same number of tickets as Beatriz if they stop at the same time.