Question

At an arcade, Jaxon and Sarah each choose a game and play the same number of times. Jaxon starts with 14 tokens and chooses a game that costs 3 tokens. Sarah starts with 10 tokens and chooses a game that costs 2 tokens. When they leave, Sarah and Jaxon have the same number of tokens. What is the number of times each person played their game?

Answer 1

To find the number of times Jaxon and Sarah played their games at the arcade, we set up an equation accounting for their starting tokens and cost per game. After solving, we find that both played their respective games 4 times.

Step-by-step explanation:

The question asks us to find the number of times Jaxon and Sarah each played their arcade games given that they end with the same number of tokens. Jaxon starts with 14 tokens and each game costs 3 tokens, while Sarah starts with 10 tokens and each game costs 2 tokens.

We need to set up an equation where the remaining tokens for both Jaxon and Sarah after playing 'n' games are equal. The equation will be:

14 - 3n = 10 - 2n

Solving this equation:

1. Add 3n to both sides: 14 = 10 - 2n + 3n
2. Combine like terms: 14 = 10 + n
3. Subtract 10 from both sides: 4 = n

Thus, Jaxon and Sarah each played their games 4 times.

Answer 2

Jaxon and Sarah each played their respective games 4 times. We found this by creating an equation based on the tokens they have left after playing, and solving for the number of plays.

Step-by-step explanation:

To determine the number of times Jaxon and Sarah each played their game, we need to set up an equation based on the number of tokens they have left.

Let's use n to represent the number of times each person played their game. Jaxon starts with 14 tokens and each game costs him 3 tokens. So after playing n times, he will have 14 - 3n tokens left. Sarah starts with 10 tokens and each game costs her 2 tokens. After playing n times, she will have 10 - 2n tokens left.

Since they both have the same number of tokens left after playing their games, we can set up the following equation:

14 - 3n = 10 - 2n

Now we can solve for n:

1. Add 3n to both sides: 14 = 10 - 2n + 3n
2. Simplify by combining like terms: 14 = 10 + n
3. Subtract 10 from both sides to solve for n: n = 14 - 10
4. n = 4

Therefore, each person played their game 4 times.