Question

The Arcade near Mary's house charges a $3 entrance fee, plus $1.25 per game played. The arcade near Evelyn's house charges a $5.50 entrance fee, plus $0.75 per game played. After how many games played will Henry and Marie spend the same amount of money?

A) 6 games
B) 9 games
C) 10 games
D) 12 games

Answer 1

To determine after how many games Henry and Marie will spend the same amount of money, we need to set up an equation. The cost of playing x games at the Arcade near Mary's house is 3 + 1.25x dollars, and the cost of playing x games at the Arcade near Evelyn's house is 5.50 + 0.75x dollars. After solving the equation, we find that they will spend the same amount of money after playing 5 games.

Step-by-step explanation:

To determine after how many games Henry and Marie will spend the same amount of money, we need to set up an equation. Let's assume they both play x number of games.

The cost of playing x games at the Arcade near Mary's house is 3 + 1.25x dollars.

The cost of playing x games at the Arcade near Evelyn's house is 5.50 + 0.75x dollars.

Setting the two costs equal to each other, we get:

3 + 1.25x = 5.50 + 0.75x

Now, we can solve this equation to find the value of x:

1.25x - 0.75x = 5.50 - 3

0.5x = 2.50

x = 5

Therefore, Henry and Marie will spend the same amount of money after playing 5 games. Therefore, the correct answer is A) 6 games.