Middle School

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Two arcades charge an entrance fee and a fee per game. At Arcade A, the total cost \( y \) (in dollars) of playing 2 games is represented by the linear function \( y = 0.75 \cdot 2 + 2 \). The table shows the total cost for playing \( x \) games at Arcade B.

\[
\begin{array}{|c|c|}
\hline
\text{Number of Games}, x & \text{Total Cost (dollars)}, y \\
\hline
0 & 8 \\
4 & 10 \\
8 & 12 \\
12 & 14 \\
\hline
\end{array}
\]

Determine which arcade is described by each phrase below.

- Higher fee per game
- Higher entrance fee
- Higher total cost for 8 games

Answer :

Answer:

Part a) Higher fee per game Arcade A

Part b) Higher entrance fee Arcade B

Part c) Higher total cost for 8 games Arcade B

Step-by-step explanation:

Let

x------> the number of games

Arcade A

we have that the linear equation is

[tex]y=0.75x+2[/tex]

The fee per game is $0.75

The entrance fee is $2

The cost for 8 games is equal to

[tex]y=0.75(8)+2=\$8[/tex]

Arcade B

Find the linear equation

Let

[tex]A(0,8),B(4,10)[/tex]

Find the slope of the line (fee per game)

[tex]m=\frac{10-8}{4-0}=0.50[/tex]

The point A is the y-intercept

The linear equation is

[tex]y=0.50x+8[/tex]

so

The fee per game is $0.50

The entrance fee is $8

The cost for 8 games is equal to

[tex]y=0.50(8)+8=\$12[/tex]

therefore

Part a) Higher fee per game Arcade A

Part b) Higher entrance fee Arcade B

Part c) Higher total cost for 8 games Arcade B

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