Adam's Arcade charges an entrance fee of $7.50 and $0.45 per game. Jim's Jamming Arcade does not charge an entrance fee, but the games are $1.25 each. How many games must be played in order for the total cost of both arcades to be the same?

To find the break-even point for the number of games played at Adam's Arcade and Jim's Jamming Arcade, set up an equation for each arcade's total cost and solve for the number of games. After setting up and solving the equation, it results in 9.375 games, meaning a player must play 10 games for the costs to be equal, rounding up since you can't play a fraction of a game.

Explanation:

To find the number of games where the total cost for both Adam's Arcade and Jim's Jamming Arcade is the same, we can set up the following equation:

Let x represent the number of games played.
Adam's Arcade: The total cost is $7.50 plus $0.45 per game, so the cost equation is 7.50 + 0.45x.
Jim's Jamming Arcade: The total cost is $1.25 per game with no entrance fee, so the cost equation is 1.25x.

Set the two equations equal to each other to find the number of games where the costs are the same:

7.50 + 0.45x = 1.25x

Subtract 0.45x from both sides:

7.50 = 0.80x

Now divide both sides by 0.80:

x = 7.50 / 0.80

x = 9.375

Since we can't play a fraction of a game, we need to round up to the nearest whole number. Therefore, the player would need to play 10 games for the total cost of both arcades to be the same.