Questions: A car service charges customers a flat fee per ride (which is higher during rush hour traffic) plus charges for each minute and each mile. Suppose that, in a certain metropolitan area during rush hour, the flat fee is 3, the cost per minute is 0.20, and the cost per mile is 1.50. Let x be the number of minutes and y the number of miles. At the end of a ride, the driver said that the passenger owed 13.50 and remarked that the number of minutes was three times the number of miles. Find the number of minutes and the number of miles for this trip. Complete the equation that represents the total cost of the ride. 0.20x + 1.50y + 3 = 13.50 Complete the equation that represents the relationship between the number of minutes and number of miles. x - 3y = 0 Find the number of minutes and the number of miles for this trip. The trip was minutes and they traveled miles.

A car service charges customers a flat fee per ride (which is higher during rush hour traffic) plus charges for each minute and each mile. Suppose that, in a certain metropolitan area during rush hour, the flat fee is 3, the cost per minute is 0.20, and the cost per mile is 1.50. Let x be the number of minutes and y the number of miles. At the end of a ride, the driver said that the passenger owed 13.50 and remarked that the number of minutes was three times the number of miles. Find the number of minutes and the number of miles for this trip. Complete the equation that represents the total cost of the ride. 0.20x + 1.50y + 3 = 13.50 Complete the equation that represents the relationship between the number of minutes and number of miles. x - 3y = 0 Find the number of minutes and the number of miles for this trip. The trip was minutes and they traveled miles.
Transcript text: A car service charges customers a flat fee per ride (which is higher during rush hour traffic) plus charges for each minute and each mile. Suppose that, in a certain metropolitan area during rush hour, the flat fee is $3, the cost per minute is $0.20, and the cost per mile is $1.50. Let $x$ be the number of minutes and $y$ the number of miles. At the end of a ride, the driver said that the passenger owed $13.50 and remarked that the number of minutes was three times the number of miles. Find the number of minutes and the number of miles for this trip. Complete the equation that represents the total cost of the ride. \[ 0.20 x+1.50 y+3=13.50 \] Complete the equation that represents the relationship between the number of minutes and number of miles. \[ x-3 y=0 \] Find the number of minutes and the number of miles for this trip. The trip was $\square$ minutes and they traveled $\square$ miles.
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Solution

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Solution Steps

Step 1: Substitute the relationship between minutes and miles into the total cost equation

To find the number of miles ($y$), we use the equation $T = F + (C_m \times (k \times y)) + (C_d \times y)$. Simplifying, we get $y = \frac{T - F}{C_m \times k + C_d} = \frac{13.5 - 3}{0.2 \times 3 + 1.5} = 5$ miles.

Step 2: Calculate the number of minutes using the relationship $x = k \times y$

Given $k = 3$, we find $x = 3 \times 5 = 15$ minutes.

Final Answer:

The trip consists of 15 minutes and 5 miles.

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