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Sagot :
Using linear functions, we have that:
a. For 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.
b. For any number of games, the cost at alley B will be less.
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 the functions in this problem, we have that:
- The slope is the cost per game.
- The intercept is the cost of 2 shoes.
Hence they are given as follows:
- A(x) = 4x + 7.5.
- B(x) = 4.5x + 5.
The cost for A will be less when:
A(x) < B(x).
Hence:
4x + 7.5 < 4.5x + 5
-0.5x < -2.5
0.5x > 2.5
x > 2.5/0.5
x > 5.
Hence for 6 or more games, the cost a bowling alley A is less, and for 4 or less games, the cost at bowling alley B is less.
For item b, with the increase of $0.5 per game, we have that:
A(x) = 4.5x + 7.5.
Then the costs per game will be the same, while alley B has the lower intercept, meaning that for any number of games, the cost at alley B will be less.
More can be learned about linear functions at https://brainly.com/question/24808124
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