To rent a car for one week, a car rental company charges a $\$ 200$ base price as well as $\$ 0.45$ per mile. Jennifer will rent a vehicle at this company, but she has a $\$ 275$ budget. Which of the following is a possible number of miles that Jennifer can drive without exceeding her budget?

Full solution

Q. To rent a car for one week, a car rental company charges a

\$ 200

base price as well as

\$ 0.45

per mile. Jennifer will rent a vehicle at this company, but she has a

\$ 275

budget. Which of the following is a possible number of miles that Jennifer can drive without exceeding her budget?

Calculate Budget Difference: Determine the amount of money available for mileage. Jennifer has a $\$275$ budget and there is a $\$200$ base price for the car rental. Subtract the base price from the total budget to find the amount available for mileage. $\$275 - \$200 = \$75$
Determine Mileage Limit: Calculate the number of miles Jennifer can drive with the remaining budget. $\newline$ The cost per mile is $\$0.45$ . To find out how many miles she can drive with the $\$75$ , divide the amount available for mileage by the cost per mile. $\newline$ $\$75 \div \$0.45$ per mile = $166.666...$ $\newline$ Since Jennifer cannot drive a fraction of a mile, we round down to the nearest whole number. $\newline$ $166.666... \approx 166$ miles
Verify Budget Limit: Verify that the calculated number of miles does not exceed the budget. Multiply the number of miles by the cost per mile and add the base price to ensure the total cost does not exceed the budget. $166$ miles $\times$ $\$$ $0$ . $45$ /mile = $\$$ $74$ . $70$ $\$$ $74$ . $70$ + $\$$ $200$ base price = $\$$ $274$ . $70$ Since $\$$ $274$ . $70$ is less than Jennifer's budget of $\$$ $275$ , she will not exceed her budget.