Question
Who wants to rent a car rental car company charges $35 per day plus $.10 per mile driven rental company be charges $25 per day plus $.15 per mile driven how many miles driven will the price charge by each company be the same miles
Answers
Answer
What will the price be for you that number of miles
Answered by
GPT-4o mini
Let's denote \( x \) as the number of miles driven.
For the first car rental company, the total cost \( C_1 \) can be expressed as:
\[
C_1 = 35 + 0.10x
\]
For the second car rental company, the total cost \( C_2 \) is:
\[
C_2 = 25 + 0.15x
\]
To find the mileage at which both companies charge the same amount, we set the two equations equal to each other:
\[
35 + 0.10x = 25 + 0.15x
\]
Now, we can solve for \( x \). First, isolate the \( x \) terms on one side:
\[
35 - 25 = 0.15x - 0.10x
\]
\[
10 = 0.05x
\]
Next, solve for \( x \) by dividing both sides by 0.05:
\[
x = \frac{10}{0.05}
\]
\[
x = 200
\]
Therefore, the price charged by each company will be the same when \( 200 \) miles have been driven.
For the first car rental company, the total cost \( C_1 \) can be expressed as:
\[
C_1 = 35 + 0.10x
\]
For the second car rental company, the total cost \( C_2 \) is:
\[
C_2 = 25 + 0.15x
\]
To find the mileage at which both companies charge the same amount, we set the two equations equal to each other:
\[
35 + 0.10x = 25 + 0.15x
\]
Now, we can solve for \( x \). First, isolate the \( x \) terms on one side:
\[
35 - 25 = 0.15x - 0.10x
\]
\[
10 = 0.05x
\]
Next, solve for \( x \) by dividing both sides by 0.05:
\[
x = \frac{10}{0.05}
\]
\[
x = 200
\]
Therefore, the price charged by each company will be the same when \( 200 \) miles have been driven.
Answered by
GPT-4o mini
To find the price for both rental companies at 200 miles driven, we can substitute \( x = 200 \) into the cost equations for each company.
### For the first rental company:
\[
C_1 = 35 + 0.10 \times 200
\]
\[
C_1 = 35 + 20
\]
\[
C_1 = 55
\]
### For the second rental company:
\[
C_2 = 25 + 0.15 \times 200
\]
\[
C_2 = 25 + 30
\]
\[
C_2 = 55
\]
Thus, the price charged by each company when driving 200 miles will be **$55**.
### For the first rental company:
\[
C_1 = 35 + 0.10 \times 200
\]
\[
C_1 = 35 + 20
\]
\[
C_1 = 55
\]
### For the second rental company:
\[
C_2 = 25 + 0.15 \times 200
\]
\[
C_2 = 25 + 30
\]
\[
C_2 = 55
\]
Thus, the price charged by each company when driving 200 miles will be **$55**.
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