MODELING REAL LIFE Bowling alley A charges $3.75 to rent shoes and $4 per game. Bowling alley B charges $2.50 torent shoes and $4.50 per game.
a. For what numbers of games is the total cost, including a pair of rental shoes, less at bowling alley A? at bowling alley B?
Bowling alley A:
Bowling alley B:
or more games
or
games
b. Bowling alley A increases the cost per game by $0.50. How does this affect your answer in part (a)? Explain.o

Using linear functions, it is found that:

a) The cheaper costs are given as follows:

• Bowling alley A: 3 or more games.

• Bowling alley B: 1 or 2 games.

b) Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

• m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

• b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For this problem, we have that:

• The cost to rent shoes is the intercept.

• The cost per game is the slope.

Hence the cost functions are given as follows:

• A(x) = 3.75 + 4x.

• B(x) = 2.5 + 4.5x.

The costs are equal when:

A(x) = B(x)

3.75 + 4x = 2.5 + 4.5x

0.5x = 1.25

x = 1.25/0.5

x = 2.5.

Hence the cheaper costs are given as follows:

• Bowling alley A: 3 or more games.

• Bowling alley B: 1 or 2 games.

Alley B has the lower initial cost due to the lower cost for the pair of shoes.

For item b, if we increase the cost per game by $0.50 for alley A, we have that:

A(x) = 4.5x + 3.75.

Hence:

Due to the same cost per game and higher cost for the pair of shoes, bowling alley A will never be cheaper than bowling alley B.

More can be learned about linear functions at brainly.com/question/24808124

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