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Bytelearn - cat image with glassesAI tutor

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To rent a car for one week, a car rental company charges a $200\$200 base price as well as $0.45\$0.45 per mile. Jennifer will rent a vehicle at this company, but she has a $275\$275 budget. Which of the following is a possible number of miles that Jennifer can drive without exceeding her budget?\newlineChoose 11 answer:\newline(A) 166166 miles\newline(B) 167167 miles\newline(C) 168168 miles\newline(D) 169169 miles

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Full solution

Q. To rent a car for one week, a car rental company charges a $200\$200 base price as well as $0.45\$0.45 per mile. Jennifer will rent a vehicle at this company, but she has a $275\$275 budget. Which of the following is a possible number of miles that Jennifer can drive without exceeding her budget?\newlineChoose 11 answer:\newline(A) 166166 miles\newline(B) 167167 miles\newline(C) 168168 miles\newline(D) 169169 miles
  1. Rephrase the problem: First, let's rephrase the ＂How many miles can Jennifer drive without exceeding her $275\$275 budget when renting a car with a $200\$200 base price and $0.45\$0.45 per mile charge?＂
  2. Calculate remaining budget: Calculate the remaining budget after the base price is subtracted from the total budget.$275\$275 budget - $200\$200 base price = $75\$75 remaining for miles
  3. Determine miles with remaining budget: Determine how many miles can be driven with the remaining $75\$75 at a rate of $0.45\$0.45 per mile.$75$0.45\frac{\$75}{\$0.45} per mile = 166166.666666...
  4. Round down to nearest whole number: Since Jennifer cannot drive a fraction of a mile for the purposes of this problem, we need to round down to the nearest whole number of miles she can drive without exceeding her budget. 166.666…166.666\ldots miles ≈166\approx 166 miles
  5. Check each answer choice: Now, let's check each answer choice to see which is the maximum number of miles she can drive without exceeding her budget.\newline(A) 166166 miles\newline(B) 167167 miles\newline(C) 168168 miles\newline(D) 169169 miles\newlineWe already know that 166166 miles is possible. Let's check if 167167 miles is possible without exceeding the budget.\newline$\$200200 base price + (167167 miles * $\$00.4545 per mile) = $\$200200 + $\$7575.1515 = $\$275275.1515
  6. Check if 167167 miles is possible: Since $275.15\$275.15 exceeds Jennifer's budget of $275\$275, she cannot drive 167167 miles. Therefore, the maximum number of miles she can drive without exceeding her budget is 166166 miles.

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