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A utility service company has a fleet of cars and trucks. The gas tank of each car has a volume of $16$ gallons, and the gas tank of each truck has a volume of $30$ gallons. If it takes $2,000$ gallons of gas to fill the empty gas tanks of the entire fleet, which equation shows the possible number of cars, $c$ , and number of trucks, $t$ , in the fleet?

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Write a linear function: word problems

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Q. A utility service company has a fleet of cars and trucks. The gas tank of each car has a volume of

16

gallons, and the gas tank of each truck has a volume of

30

gallons. If it takes

2,000

gallons of gas to fill the empty gas tanks of the entire fleet, which equation shows the possible number of cars,

c

, and number of trucks,

t

, in the fleet?

Identify variables: Identify the variables and their relationship. $\newline$ Each car has a $16$ -gallon gas tank, and each truck has a $30$ -gallon gas tank. The total volume of gas needed to fill all the vehicles in the fleet is $2,000$ gallons. We need to find an equation that relates the number of cars ( $c$ ) and the number of trucks ( $t$ ) to the total volume of gas.
Write equation: Write the equation based on the given information. $\newline$ The total volume of gas used by the cars is $16$ gallons per car times the number of cars. The total volume of gas used by the trucks is $30$ gallons per truck times the number of trucks. The sum of these two amounts should equal the total volume of gas needed, which is $2,000$ gallons. $\newline$ So, the equation is: $16c + 30t = 2,000$ .

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