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18. A certain arcade charges 5¢ for each game and a [tex]$5.00[/tex] entry fee.

a) Write a function that models the cost \(C\) for playing \(x\) games.

b) How much does it cost to play 80 games?

c) How many games can be played if you bring a [tex]$20[/tex] bill?

Answer :

Let's work through the problem step by step.

### a) Write a function that models the cost [tex]\( C \)[/tex] for playing [tex]\( x \)[/tex] games.

To model the cost, we need to consider both the entry fee and the cost per game.

- The entry fee is [tex]\( \$5.00 \)[/tex].
- Each game costs [tex]\( 5 \)[/tex] cents, which is [tex]\( \$0.05 \)[/tex].

The total cost [tex]\( C \)[/tex] for playing [tex]\( x \)[/tex] games can be expressed by the function:

[tex]\[ C(x) = 5 + 0.05x \][/tex]

Here, [tex]\( C(x) \)[/tex] gives us the total cost in dollars.

### b) How much does it cost to play 80 games?

Using the function [tex]\( C(x) = 5 + 0.05x \)[/tex], we substitute [tex]\( x = 80 \)[/tex]:

[tex]\[ C(80) = 5 + 0.05 \times 80 \][/tex]

First, calculate [tex]\( 0.05 \times 80 \)[/tex]:

[tex]\[ 0.05 \times 80 = 4 \][/tex]

Now, add the entry fee:

[tex]\[ C(80) = 5 + 4 = 9 \][/tex]

So, the cost to play 80 games is [tex]\( \$9.00 \)[/tex].

### c) How many games can be played if you bring a [tex]$20 bill?

You have \( \$[/tex]20.00 \) to spend. First, subtract the entry fee from this amount:

[tex]\[ 20 - 5 = 15 \][/tex]

After paying the entry fee, you have [tex]\( \$15.00 \)[/tex] left for playing games. Each game costs [tex]\( \$0.05 \)[/tex]. To find out how many games you can play, divide the remaining money by the cost per game:

[tex]\[ \text{Number of games} = \frac{15}{0.05} \][/tex]

Perform the division:

[tex]\[ \frac{15}{0.05} = 300 \][/tex]

So, with a $20 bill, you can play 300 games.

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