Final answer:
The correct equation to find the number of games where the cost is the same at Adam's Arcade and Jim's Jamming Arcade is 7.50 + 0.45x = 1.25x. After solving the equation, the number of games played should be 10 for the costs to be approximately the same.
Step-by-step explanation:
To find the number of games that must be played for the total cost at Adam's Arcade and Jim's Jamming Arcade to be the same, you need to set up an equation where the total cost of both arcades is equal. Let's use x to represent the number of games played.
For Adam's Arcade, the total cost is the entrance fee plus the cost per game times the number of games, which is 7.50 + 0.45x. For Jim's Jamming Arcade, since there is no entrance fee, the cost is just the price per game times the number of games, 1.25x.
To find when these costs are equal, you write the equation: 7.50 + 0.45x = 1.25x. Now, you can solve for x to find the number of games where the cost will be the same at both arcades. Subtract 0.45x from both sides to isolate x on one side: 7.50 = 0.80x. Finally, divide both sides by 0.80 to find the number of games: x = 9.375. Since you cannot play a fraction of a game, you would round up to say that after 10 games, the total cost at both arcades begins to become similar.