Final answer:
Using algebra, we find that Stacey and Robin will have the same amount of money remaining after 8 games. This is determined by setting up equations that represent the amount of money each person has after a certain number of games and solving for when those amounts are equal.
Step-by-step explanation:
Stacey and Robin are playing games in an arcade and we want to find out after how many games they will have the same amount of money remaining. Stacey started with $15 and spends $0.75 per game, while Robin started with $13 and spends $0.50 per game. To solve this, we can set up an equation where the total amount of money each has left is the same after a certain number of games.
For Stacey: $15 - $0.75x = remaining money after x games.
For Robin: $13 - $0.50x = remaining money after x games.
Setting these two expressions equal to find the value of x when both have the same amount of money left, we get:
$15 - $0.75x = $13 - $0.50x
Moving the variables to one side and the constants to the other side gives us:
$0.75x - $0.50x = $13 - $15
Combining like terms, we get:
$0.25x = -$2
Dividing both sides by $0.25 to solve for x gives us:
x = -$2 / $0.25
x = 8
Thus, after 8 games, Stacey and Robin will have the same amount of money remaining.