Question

The total cost for bowling includes the fee for show rental plus a fee per game. the cost of each game increases the price by $4. After 3 games the total cost with shoe rental is $14

a. write an equation to represent the total cost y to rent shoes and bowl x games.
b. how much is shoe rentals? how is it represented in the equation?

Answer 1

The student's question about the cost of bowling can be expressed by the linear equation y = 2 + 4x, where y is the total cost and x is the number of games played. The shoe rental fee is $2 and it is represented as the constant term in the linear equation.

Step-by-step explanation:

The total cost y for bowling can be represented by a linear equation that includes a fixed shoe rental fee plus a variable fee per game. Given that the cost increases by $4 per game and the total cost after 3 games including shoe rental is $14, we can express the relationship as follows:

• y = shoe rental fee + ($4 × number of games)
• y = shoe rental fee + ($4 × x)
• For 3 games (x = 3), the total cost y is $14.

We can use this information to find out the shoe rental fee by plugging in the values for y and x:

$14 = shoe rental fee + ($4 × 3)

$14 = shoe rental fee + $12

Shoe rental fee = $14 - $12

Shoe rental fee = $2

The shoe rental cost is represented in the equation as the constant term that is added to the cost per game.

Answer 2

a) y + 4x = 14

To find the cost of the shoe rental (represented as y), we plug in the number of games and isolate the y:

y + 4x = 14 We plug in 3 for x because they bowled 3 games:
y + 4(3) = 14 Then, multiply:
y + 12 = 14 Subtract 12 on each side to isolate the y:
y = 2

b) So, the cost of shoe rentals is $2.