Lucia rented a car for $211 per week (withunlimited driving miles) to use during

Question

Lucia rented a car for $211 per week (withunlimited driving miles) to use during her spring break vacation. She must also pay for gasoline which costs $3.65 per gallon. The gas mileage of the car is 30 miles per gallon (mpg) on average.

a. What quantities are changing in this situation? What quantities are not changing?

b. i. If Lucia traveled 100 miles, how many gallons of gasoline didi she use?

ii. If Lucia traveled 200 miles, how many gallons of gasoline didi she use?

iii. If Lucia traveled 500 miles, how many gallons of gasoline didi she use?

c. Define a formula to determine the number of gallons gasoline n in term of the number of miles driven x.

d. Define a formula to determine the cost of gasoline c in term of the number of gallon of gasoline used.

e. Define a formula to determine the total cost T of driving the rental car x miles, including the one week rental cost of $211.

f. How much does the total rental cost increase for each 100 miles the car is driven during the rental period. Explain you reason.

g. How much does the total rental cost increase for each mile driven? Explain the thinking you used to arrive at your answer.

Explanation / Answer

The $211 per week is unchanging as this is the fixed cost
per week that must be paid. The cost of fuel of $3.65 per gn is also
not changing.

The quantities changing are
gas mileage(there will be slight changes to this)
and the number of miles covered .

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b) i) 100/30 = 10/3 gallons used
ii) 200/30 = 20/3 gallons used
iii) 500/30 = 50/3 gallons used

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c)
n = x/30

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d)
c = 3.65n

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e)
T = fixed cost + variable cost

T = 211 + 3.65*x/30

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f)
The total rental cost only depends on the no of miles travelled...
Initially when x = 0, T = 211
And when x = 100, T = 211 + 3.65*100/30 = 223.1666666666666667

So, for each 100 miles driven, the cost
increases by approx 12.17 dollars

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g) For each mile drievn,
the increase is by a factor of 3.65/30 as in approx 0.12 dollars
It is exactly 73/600 dollar increasefor each mile drievn

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