Math

QuestionSelect two fractions that, when multiplied, yield the cost per mile to drive, rounding to the nearest cent:
1 gallon / 2.30 dollars 2.30 dollars / 1 gallon 24 miles / 1 gallon 1 gallon / 24 miles
Find the cost in \$ per mile.

Studdy Solution

STEP 1

Assumptions1. The cost of gasoline is $.30 per gallon. The car can travel24 miles per gallon3. We are looking for the cost in dollars to drive each mile4. We are using dimensional analysis to solve this problem5. The units of the fractions we choose must cross-cancel to produce the unit of our desired answer

STEP 2

First, we need to select the two fractions that when multiplied together will give us the cost per mile. The units of the fractions we choose must cross-cancel to produce the unit of our desired answer, which is dollars per mile.

STEP 3

The first fraction we choose is the cost of gasoline, which is 2.30pergallon.Thiscanbewrittenas2.30 per gallon. This can be written as2.30dollars1gallon\frac{2.30\, dollars}{1\, gallon}$

STEP 4

The second fraction we choose is the distance the car can travel per gallon, which is24 miles per gallon. However, we need to invert this fraction so that the gallons unit will cancel out when we multiply the two fractions. This can be written as1gallon24miles\frac{1\, gallon}{24\, miles}

STEP 5

Now, we multiply the two fractions together. The gallons unit in the numerator of the first fraction and the gallons unit in the denominator of the second fraction will cancel out, leaving us with the unit of dollars per mile.
2.30dollars1gallon×1gallon24miles=2.30dollars24miles\frac{2.30\, dollars}{1\, gallon} \times \frac{1\, gallon}{24\, miles} = \frac{2.30\, dollars}{24\, miles}

STEP 6

Finally, we calculate the cost per mile by dividing2.30 dollars by24 miles.
2.30dollars24miles=0.0958dollarspermile\frac{2.30\, dollars}{24\, miles} =0.0958\, dollars\, per\, mile

STEP 7

Round your answer to the nearest cent.
0.095dollarspermile0.10dollarspermile0.095\, dollars\, per\, mile \approx0.10\, dollars\, per\, mileThe cost to drive each mile is approximately $0.10.

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