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Answer :
Sure! Let's work through the problem step-by-step to find the correct equation that can be used.
### Problem Details:
- Rental Fee: There is a fixed fee of [tex]$45 to rent the machine.
- Total Spent: Tristanne spent a total of $[/tex]137 on the rental.
- Daily Cost: The cost of renting the machine per day is [tex]$23.
- Goal: Find an equation to represent this situation and determine how many days Tristanne rented the machine for.
### Understanding the Scenario:
When Tristanne rents the machine, she has to pay a $[/tex]45 fee upfront. In addition to this, she pays [tex]$23 for each day she rents the machine. Together, these costs total to $[/tex]137.
### Formulating the Equation:
1. Daily Costs Contribution:
- Let's denote the number of days the machine is rented as [tex]\( d \)[/tex].
- The cost just for renting the machine per day is [tex]\( 23d \)[/tex] (since it's [tex]$23 per day).
2. Total Cost Equation:
- Add the daily costs to the initial fee to find the total cost.
- The total cost can be represented by the equation:
\[
23d + 45 = 137
\]
- Here, \( 23d \) represents the daily rental cost over \( d \) days and $[/tex]45 is the initial rental fee.
### Conclusion:
The equation [tex]\( 23d + 45 = 137 \)[/tex] accurately represents the total expenditure for renting the rug-cleaning machine, including both the flat fee and the daily expenses.
This aligns with option 2 from the choices provided, which correctly describes the situation.
### Problem Details:
- Rental Fee: There is a fixed fee of [tex]$45 to rent the machine.
- Total Spent: Tristanne spent a total of $[/tex]137 on the rental.
- Daily Cost: The cost of renting the machine per day is [tex]$23.
- Goal: Find an equation to represent this situation and determine how many days Tristanne rented the machine for.
### Understanding the Scenario:
When Tristanne rents the machine, she has to pay a $[/tex]45 fee upfront. In addition to this, she pays [tex]$23 for each day she rents the machine. Together, these costs total to $[/tex]137.
### Formulating the Equation:
1. Daily Costs Contribution:
- Let's denote the number of days the machine is rented as [tex]\( d \)[/tex].
- The cost just for renting the machine per day is [tex]\( 23d \)[/tex] (since it's [tex]$23 per day).
2. Total Cost Equation:
- Add the daily costs to the initial fee to find the total cost.
- The total cost can be represented by the equation:
\[
23d + 45 = 137
\]
- Here, \( 23d \) represents the daily rental cost over \( d \) days and $[/tex]45 is the initial rental fee.
### Conclusion:
The equation [tex]\( 23d + 45 = 137 \)[/tex] accurately represents the total expenditure for renting the rug-cleaning machine, including both the flat fee and the daily expenses.
This aligns with option 2 from the choices provided, which correctly describes the situation.
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