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Math

QuestionTran pays \84forgasanddrives84 for gas and drives m$ miles.
a) Find the cost per mile. b) What does "per" mean? c) Test with m=200m = 200. Does it make sense?

Studdy Solution

STEP 1

Assumptions1. The cost to fill the truck with gas is 84.Thetruckcandrive84. The truck can drive m$ miles on a full tank3. We are looking for the cost per mile

STEP 2

To find the cost per mile, we need to divide the total cost by the number of miles. This gives us an expression for the cost per mile.
Cost per mile=Total costNumber of milesCost\, per\, mile = \frac{Total\, cost}{Number\, of\, miles}

STEP 3

Now, plug in the given values for the total cost and the number of miles to get the expression for the cost per mile.
Cost per mile=$84mCost\, per\, mile = \frac{\$84}{m}

STEP 4

The word "per" in the phrase "cost per mile" indicates division. This is because "per" is used to indicate a rate or ratio, dividing the total quantity by the number of units.

STEP 5

To check the expression, we substitute200 miles for mm in the expression for the cost per mile.
Cost per mile=$84200Cost\, per\, mile = \frac{\$84}{200}

STEP 6

Calculate the cost per mile when m=200m =200.
Cost per mile=$84200=$0.42Cost\, per\, mile = \frac{\$84}{200} = \$0.42This means that for every mile Tran drives, he spends $0.42 on gas. This makes sense as the cost per mile should be less than the total cost of gas.

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