To solve the problem, let's start by setting up the right equation based on the information provided.
We need to find how much the agency charges per day, denoted as [tex]\( d \)[/tex].
1. Identify the relevant information from the problem:
- The total cost for 9 days is \[tex]$920.
- There is a one-time discount of \$[/tex]25.
2. Given the choices for the equation:
[tex]\[ 9d - 25 = 920 \][/tex]
[tex]\[ 25(d - 9) = 920 \][/tex]
[tex]\[ 25d - 9 = 920 \][/tex]
[tex]\[ 9(d - 25) = 920 \][/tex]
3. Choose the correct equation:
The equation must account for the total number of days (9) and the one-time discount (\[tex]$25) off the total cost (\$[/tex]920). The equation [tex]\( 9d - 25 = 920 \)[/tex] reflects this accurately: it takes the daily cost [tex]\( d \)[/tex], multiplies it by 9 days, and then subtracts the \[tex]$25 discount, setting the result equal to \$[/tex]920.
4. Solve the equation to find [tex]\( d \)[/tex]:
[tex]\[ 9d - 25 = 920 \][/tex]
Add 25 to both sides of the equation to isolate the term with [tex]\( d \)[/tex]:
[tex]\[ 9d = 920 + 25 \][/tex]
[tex]\[ 9d = 945 \][/tex]
Divide both sides by 9 to solve for [tex]\( d \)[/tex]:
[tex]\[ d = \frac{945}{9} \][/tex]
[tex]\[ d = 105 \][/tex]
So, the equation used is:
[tex]\[ 9d - 25 = 920 \][/tex]
And, the agency charges [tex]\( \$105 \)[/tex] per day.
