the cote family car gets between 25 and 29 miles per gallon of gasoline the fuel tank holds 17 gallons of gasoline and the cotes refill the tank whenever it is 1/4

full the cost of gasoline will be 3.47 and 3.69 per gallon
A) write expressions to estimate the amount they will pay for gasoline and the number of times they will need to stop for gas for a trip of m miles. Justify the choice of numbers you use In your expressions.
B) Denver 1004 miles from Chicago. For a round trip from Denver to Chicago, how much should they budget for gas? How many times can they expect to stop for gas on the trip? Explain your reasoning.

Four gallons of gasoline cost $14. How much does each gallon of gasoline cost?

A) To estimate the amount the Cote family will pay for gasoline, we can use the following expression:

Amount paid for gasoline = Number of stops for gas * Cost per gallon * Number of gallons refilled

To estimate the number of times they will need to stop for gas for a trip of m miles, we can use the following expression:

Number of stops for gas = (m / mpg) / (tank size * (3/4))

In this expression, we divide the total distance of the trip by the miles per gallon (mpg) to determine the number of gallons needed. Then we divide this by the tank size multiplied by (3/4) to account for the 1/4 full refueling strategy.

B) For a round trip from Denver to Chicago, we need to calculate the total cost of gas and the number of stops for gas.

Total cost of gas = Amount paid for gasoline * 2
Number of stops for gas = Number of stops for gas * 2

We multiply the amount paid for gas by 2 to account for the round trip, and likewise for the number of stops for gas. This assumes that the car's mileage and fuel efficiency remain constant throughout the trip.

It's important to note that to properly calculate the values m, mpg, tank size, and cost per gallon, we would need more information from the question or certain assumptions.

A) To estimate the amount the Cote family will pay for gasoline on a trip of m miles, we need to consider the fuel efficiency range of their car and the price of gasoline.

1. Let's start with the fuel efficiency range of their car. The Cote family's car gets between 25 and 29 miles per gallon of gasoline. We can use the average of this range to estimate their car's fuel efficiency. The average of 25 and 29 is (25 + 29) / 2 = 27 mpg. So, their car's fuel efficiency can be approximated as 27 miles per gallon.

2. Now, we need to consider the cost of gasoline. The prices mentioned are $3.47 and $3.69 per gallon. To estimate the amount they will pay for gasoline, we can take the average of these prices. The average of $3.47 and $3.69 is ($3.47 + $3.69) / 2 = $3.58 per gallon.

3. To calculate the amount they will pay for gasoline, we can set up the expression:
Amount they will pay for gasoline = (m miles) / (fuel efficiency) * (price per gallon)
Substituting the values we have:
Amount they will pay for gasoline = (m) / (27) * ($3.58)

4. The number of times they will need to stop for gas can be approximated by dividing the total distance of the trip by the range (number of miles on a full tank):
Number of times they will stop for gas = (m miles) / (range of miles on a full tank)
Substituting the values we have:
Number of times they will stop for gas = (m) / (17 * 27)

B) For a round trip from Denver to Chicago, we can calculate the total distance as twice the distance between the two cities:
Total distance = 2 * 1004 miles = 2008 miles

To calculate how much they should budget for gas, we will use the expression we derived in part A:
Amount they will pay for gasoline = (m) / (27) * ($3.58)
Substituting the total distance:
Amount they should budget for gas = (2008 miles) / (27) * ($3.58)

To calculate how many times they can expect to stop for gas, we will use the expression derived in part A:
Number of times they will stop for gas = (m) / (17 * 27)
Substituting the total distance:
Number of times they can expect to stop for gas = (2008 miles) / (17 * 27)

The reasoning behind these calculations is that we use the average fuel efficiency and gas prices to estimate the amount they will pay for gasoline. We then divide the total distance by the range of miles on a full tank to approximate the number of times they will stop for gas.

https://www.jiskha.com/display.cgi?id=1509143037