Ben's Video shack charges $1.50 to rent a video game for a night. Mr. Gareth's Entertainments charges $5.00 plus $0.50 per night for a game.

For how many nights is the cost the same for both stores?

Answer: 5 nights

Step-by-step explanation: Mr. Gareth's Entertainments has a one time fee of $5.00, then charges $0.50 per night for a game, while Ben's Video shack charges $1.50 to rent a video game for a night. We can set up equations for both places. We can let x = the amount of nights the game is being rented for. Mr. Gareth's Entertainments = $0.50x + $5.00 because $0.50 is being charged every night and $5.00 was charged only once. Ben's Video shack = $1.50x. We can make the equations equal to eachother, so $1.50x = $0.50x + $5.00

We can subtract by $0.50x both sides to make it so only one side will have x. This will make the equation easier to solve. By subtracting $0.50x from both sides, we get $1.00x = $5.00. Since we made x = the amount of nights the game is being renmted for, we know x = 5, so it would take 5 nights.

We can double check. $1.50 * 5 = $7.50

$0.50 * 5 = $2.50

$2.50 + $5 = $7.50