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 3.46 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.
A. d = 2 * 1004 = 2008 miles.
2008mi/(25mi/gal) = 80.32 gal, max required.
B. 80.32gal * 3.69/gal = $296.38 = Budget for gas.
They fill-up each time they use 3/4 of a tank of gas(12.75 gal).
12.75gal * 25mi/gal = 318.75 miles/fill-up.
2008mi/(318.75mi/fill-up) = 6.3 or 7 fill-ups for the round trip.
A) To estimate the amount the Cote family will pay for gasoline for a trip of m miles, we can break it down into two parts:
1) Expression to estimate the number of times they will need to stop for gas:
Let's assume that the Cote family stops for gas when the tank is 1/4 full. Since the fuel tank holds 17 gallons, the Cotes will refill the tank when it reaches 17 * 1/4 = 4.25 gallons.
When the tank is 1/4 full, they would have used 17 - 4.25 = 12.75 gallons of fuel. Based on the given fuel efficiency range of 25-29 miles per gallon, we can estimate that they can travel approximately 12.75 * 25 = 318.75 miles to 12.75 * 29 = 370.5 miles before needing to stop for gas.
Therefore, the number of times they will need to stop for gas can be estimated using the equation: Number of stops ≈ m / (318.75 to 370.5)
2) Expression to estimate the amount they will pay for gasoline:
To estimate the amount they will pay for gasoline, we need to consider the cost per gallon. The cost of gasoline is given as $3.46 to $3.69 per gallon.
Let's assume that they pay the highest price per gallon, which is $3.69. The amount they will pay for one refill is 4.25 * $3.69 = $15.69.
Considering the estimated number of stops calculated in step 1, the total amount they will pay for gasoline can be estimated as Total cost ≈ Number of stops * $15.69.
B) To determine the budget for gas for a round trip from Denver to Chicago, which is 1004 miles away, we can use the expressions derived in part A.
1) Budget for gas:
Using the expression Total cost ≈ Number of stops * $15.69, we need to calculate the estimated number of stops for the round trip:
Number of stops ≈ (1004 * 2) / (318.75 to 370.5) ≈ 6.79 to 7.92 stops.
Therefore, the estimated budget for gas for the round trip is approximately $15.69 * 7.92 = $124.33 to $15.69 * 6.79 = $106.46.
2) Number of expected stops:
Based on the calculation above, they can expect to make approximately 6.79 to 7.92 stops during the round trip.
This estimation is based on the given fuel efficiency range, assuming a constant rate of consumption, and considering the maximum price per gallon.
A) To estimate the amount the Cote family will pay for gasoline, we can break it down into two parts: the number of times they will need to refill the tank and the cost per gallon.
1. Number of times to refill the tank:
The fuel tank holds 17 gallons of gasoline, and the Cotes refill the tank whenever it is 1/4 full. So when the tank is 1/4 full, they have 17/4 gallons remaining. Each time they refill the tank, they will have used up 17 - (17/4) gallons of gasoline.
2. Cost per gallon:
The cost of gasoline is given as $3.46 and $3.69 per gallon. Since the actual value is not specified, we can choose the average of these two values, which is ($3.46 + $3.69) / 2 = $3.575 per gallon.
Now we can write the expression for the amount they will pay for gasoline:
Amount paid for gasoline = (Number of times to refill the tank) * (Gallons used per refill) * (Cost per gallon)
B) For the round trip from Denver to Chicago, we are given that the distance is 1004 miles.
To estimate the amount they should budget for gas, we need to determine the total number of gallons needed for the trip, and then multiply it by the chosen cost per gallon.
1. Total number of gallons needed:
To estimate the total number of gallons needed for a certain distance, we can use the average mileage per gallon given. The car gets between 25 and 29 miles per gallon, so we can choose the average of these two values as well: (25 + 29) / 2 = 27 miles per gallon.
So, the total number of gallons needed for the round trip would be:
Total gallons needed = (Total distance) / (Miles per gallon) = 1004/27 gallons.
2. The number of times to stop for gas:
To determine the number of times they can expect to stop for gas on the trip, we can find how many times they will need to refill the tank. Refilling the tank is required whenever it is 1/4 full.
Number of times to stop for gas = (Total gallons needed) / (Gallons used per refill).
Since we already know the number of times to refill the tank from part A, we can use that expression here as well.
By using the expressions derived in part A and part B, we can calculate the estimated cost for gas and the expected number of stops for the Cote family.