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Answer :
To determine which equation can be used to find the number of days Tristanne rented the rug-cleaning machine, let's break down the information provided:
1. Form Fee: Tristanne paid a form fee of [tex]$45.
2. Total Rent Cost: The total cost for renting the machine was $[/tex]137.
3. Daily Rent Cost: The daily rent cost is [tex]$23.
We need an equation that involves the number of days, represented by \( d \), Tristanne rented the machine.
Start by setting up the equation:
1. Daily Rent Contribution: Each day Tristanne rents the machine, she pays $[/tex]23. Thus, the cost from renting for [tex]\( d \)[/tex] days is [tex]\( 23d \)[/tex].
2. Adding the Form Fee: In addition to the daily rent, she also paid a form fee of [tex]$45.
Combining these, the total cost can be expressed as:
\[ 23d + 45 = 137 \]
This equation includes the form fee, the daily rent cost, and matches the total amount Tristanne spent, $[/tex]137.
Now, solve the equation:
1. Subtract the form fee from the total cost to find the total daily rental cost:
[tex]\[ 137 - 45 = 23d \][/tex]
2. Solve for [tex]\( d \)[/tex] by dividing the remaining total cost by the daily rate:
[tex]\[ d = \frac{137 - 45}{23} \][/tex]
This calculation shows that Tristanne rented the machine for 4 days.
So, the correct equation is:
[tex]\[ 23d + 45 = 137 \][/tex]
1. Form Fee: Tristanne paid a form fee of [tex]$45.
2. Total Rent Cost: The total cost for renting the machine was $[/tex]137.
3. Daily Rent Cost: The daily rent cost is [tex]$23.
We need an equation that involves the number of days, represented by \( d \), Tristanne rented the machine.
Start by setting up the equation:
1. Daily Rent Contribution: Each day Tristanne rents the machine, she pays $[/tex]23. Thus, the cost from renting for [tex]\( d \)[/tex] days is [tex]\( 23d \)[/tex].
2. Adding the Form Fee: In addition to the daily rent, she also paid a form fee of [tex]$45.
Combining these, the total cost can be expressed as:
\[ 23d + 45 = 137 \]
This equation includes the form fee, the daily rent cost, and matches the total amount Tristanne spent, $[/tex]137.
Now, solve the equation:
1. Subtract the form fee from the total cost to find the total daily rental cost:
[tex]\[ 137 - 45 = 23d \][/tex]
2. Solve for [tex]\( d \)[/tex] by dividing the remaining total cost by the daily rate:
[tex]\[ d = \frac{137 - 45}{23} \][/tex]
This calculation shows that Tristanne rented the machine for 4 days.
So, the correct equation is:
[tex]\[ 23d + 45 = 137 \][/tex]
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