Question

A bowling alley charges $2.00 per game and will rent a pair of shoes for $1.00 for any number of games. The bowling alley has an earnings goal of $300 for the day.

a. Write a linear equation that describes the problem.
b. If the bowling alley rents 40 pairs of shoes, how many games will need to be played to reach its goal?

a) Linear equation: Earnings = 2Games + 1Shoe Rentals
b) 120 games
c) 80 games
d) 40 games

Answer 1

The linear equation to describe the problem is Earnings = 2 × Number of games + 1 × Number of shoe rentals. To reach the earnings goal of $300 with 40 shoe rentals, the bowling alley must have 130 games played.

Step-by-step explanation:

To solve this problem, we need to create a linear equation that represents the earnings of the bowling alley from both the games and shoe rentals. The question states that each game costs $2.00 and each pair of shoes costs $1.00 to rent. The earnings goal is $300. Using these details, we can write the linear equation as:

Earnings = 2 × Number of games + 1 × Number of shoe rentals

This can also be represented as E = 2G + S, where E represents the total earnings, G represents the number of games, and S represents the number of shoe rentals.

Now, we know that the bowling alley rents 40 pairs of shoes. Therefore, substituting S = 40 into the equation, we get:

E = (2 × G) + (1 × 40)

Since the earnings goal is E = $300, we can solve for G as follows:

300 = 2G + 40
260 = 2G
130 = G

So, the bowling alley needs to rent 40 pairs of shoes and have 130 games played to reach its earnings goal of $300, making option (b) 120 games incorrect and our solution indicating a different number of games required.