Julia and Kevin are playing games at the arcade. Julia started with $15, and the machine she is playing costs $0.75 per game. Kevin started with $13, and his machine costs $0.50 per game. After how many games will these two kids have the same amount of money remaining?

Set up an equation and solve.

15-.75x = 13-.50x

Now just find x

15 - 3/4 x = 13 - 1/2 x
60-3x = 52-2x
8 = x

After 8 games,
Julia has 15-8*.75 = 15-6 = $9.00
Kevin has 13-8*.50 = 13-4 = $9.00

To find out how many games it will take for Julia and Kevin to have the same amount of money remaining, we can set up an equation.

Let's say \(x\) represents the number of games they play. For Julia, the amount she has remaining after playing \(x\) games would be \(15 - 0.75x\). Similarly, for Kevin, the amount he has remaining after playing \(x\) games would be \(13 - 0.50x\).

To find when they have the same amount remaining, we set the two expressions equal to each other and solve for \(x\):
\[15 - 0.75x = 13 - 0.50x.\]

Let's solve this equation:
\[15 - 0.75x = 13 - 0.50x.\]

First, we can simplify by combining like terms:
\[0.25x = 2.\]

To isolate \(x\), we divide both sides of the equation by 0.25:
\[x = \frac{2}{0.25}.\]

Dividing 2 by 0.25, we get:
\[x = 8.\]

Therefore, it will take 8 games for Julia and Kevin to have the same amount of money remaining.