Question

As the school's security officer, Joey gets paid $35.50 for every football game that he attends. He also gets paid $42 per soccer game that he attends. Joey earns $991 for 27 paid events. Write a system of equations, describe each variable, and solve. How many football games did he attend?

Answer 1

Let x represent the number of football games Joey attended, and y represent the number of soccer games he attended. Based on the given information, the system of equations can be formed as follows:

35.50x + 42y = 991 (equation representing the total amount earned from attending games)

x + y = 27 (equation representing the total number of games attended)

Solving this system of equations yields the number of football games Joey attended.

Step-by-step explanation:

To formulate the system of equations, let x denote the number of football games attended by Joey, and y denote the number of soccer games attended. The total amount Joey earns from attending games can be expressed as 35.50x (for football games) + 42y (for soccer games), equating to his total earnings of $991 for 27 games attended. This relationship is expressed by the equation 35.50x + 42y = 991.

Additionally, the total number of games attended by Joey is 27, encompassing both football and soccer games. This is represented by the equation x + y = 27, signifying the total count of games Joey participated in.

By solving this system of equations simultaneously, we can ascertain the number of football games Joey attended. Utilizing methods like substitution, elimination, or graphing, we can solve the system of equations. The objective is to find the specific value of x, representing the number of football games, and y, representing the number of soccer games, satisfying both equations simultaneously. This process reveals the number of football games Joey attended among the 27 paid events.