To determine the correct equation for the charges [tex]\( C \)[/tex] in terms of the number of buckets of balls [tex]\( b \)[/tex] used at a golf driving range, we need to consider the following information:
1. There is a flat fee of \[tex]$20 to practice.
2. There is an additional cost of \$[/tex]5.75 for each bucket of balls.
Let's break this down:
- The flat fee is a constant amount, \[tex]$20, which you pay regardless of how many buckets of balls you use.
- For every bucket of balls you use, you pay an additional \$[/tex]5.75.
Therefore, the total charges [tex]\( C \)[/tex] will be the sum of the flat fee and the cost for the buckets of balls.
### Step-by-Step Solution:
1. Flat Fee: The flat fee is \[tex]$20.
2. Cost per Bucket: For each bucket of balls, the cost is \$[/tex]5.75. If you use [tex]\( b \)[/tex] buckets of balls, the cost for the buckets will be [tex]\( 5.75b \)[/tex].
3. Total Charges: The total charges [tex]\( C \)[/tex] will be the flat fee plus the cost for the buckets of balls. The equation representing this relationship is:
[tex]\[ C = 20 + 5.75b \][/tex]
Now, let's match this equation to the options provided:
A. [tex]\( C = 5750 + 20 \)[/tex]
- This equation is incorrect as it does not include the variable [tex]\( b \)[/tex], and 5750 is far too large.
B. [tex]\( c = 20 b + 5.75 \)[/tex]
- This equation is incorrect since it incorrectly multiplies 20 by [tex]\( b \)[/tex] and adds a constant 5.75.
C. [tex]\( b = 575 C + 20 \)[/tex]
- This equation is incorrect since it incorrectly isolates [tex]\( b \)[/tex] and improperly scales [tex]\( C \)[/tex] by 575.
D. [tex]\( b = 20 C + 5.75 \)[/tex]
- This equation is incorrect as it incorrectly scales [tex]\( C \)[/tex] by 20 and improperly adds 5.75 to [tex]\( C \)[/tex].
E. [tex]\( b = 575 c \cdot 20 \)[/tex]
- This equation is incorrect since it mistakenly translates the units and incorrectly multiplies and scales [tex]\( C \)[/tex] and [tex]\( b \)[/tex].
Only option [tex]\( \boxed{C = 20 + 5.75b} \)[/tex] models the charges [tex]\( C \)[/tex] correctly in terms of the number of buckets of balls [tex]\( b \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{C = 20 + 5.75b} \][/tex]
