Math Problem Statement

You can fill a 15​-gallon tank of gas for ​$38.03 or buy gas for ​$2.50​/gallon.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The better deal is to fill a 15/ gallon tank for $ 38.03 because the price to fill a 15​-gallon tank of gas for ​$38.03 is ​how much per gallon. B. The better deal is to buy gas for $ 2.50/gallon because the price to fill a 15​-gallon tank of gas for ​$38.03 is how much per gallon. ​(Round to the nearest cent as​ needed.)

Solution

Let's first calculate the price per gallon if you fill a 15-gallon tank for $38.03.

To find the price per gallon, divide the total cost by the number of gallons:

Price per gallon=38.03152.5353dollars per gallon\text{Price per gallon} = \frac{38.03}{15} \approx 2.5353 \, \text{dollars per gallon}

Rounding to the nearest cent, the price per gallon is $2.54.

Now, let's compare the two options:

  • Filling the 15-gallon tank for $38.03 results in a price of $2.54 per gallon.
  • Buying gas for $2.50 per gallon is obviously cheaper.

So, the better deal is to buy gas for $2.50 per gallon.

The correct choice is:

B. The better deal is to buy gas for $2.50/gallon because the price to fill a 15-gallon tank of gas for $38.03 is $2.54 per gallon.

Would you like more details or have any questions? Here are 5 related questions for further exploration:

  1. How much money would you save by choosing the cheaper option over 15 gallons?
  2. If gas prices fluctuate, how do you determine the break-even point between two prices?
  3. What is the total cost if you buy gas for $2.50 per gallon and need to fill a 20-gallon tank?
  4. How much would it cost to fill a 15-gallon tank if the price per gallon is $3.10?
  5. If gas prices increase by 5%, how does that impact the total cost of a 15-gallon refill?

Tip: Always check the per-unit price when comparing deals—small differences can add up over time!

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Math Problem Analysis

Mathematical Concepts

Unit Rates
Division

Formulas

Price per gallon = Total cost / Number of gallons

Theorems

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Suitable Grade Level

Grades 5-7