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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?
Choose 1 answer:
(A)
16 t+30 c=2,000
(B)
30 t+16 c=2,000
(C)
t+30 c=2,000
(D)
t+16 c=2,000

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? $\newline$ Choose $1$ answer: $\newline$ (A) $16 t+30 c=2,000$ $\newline$ (B) $30 t+16 c=2,000$ $\newline$ (C) $t+30 c=2,000$ $\newline$ (D) $t+16 c=2,000$

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Solve a system of equations using any method: word problems

Full solution

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?

\newline

Choose

1

answer:

\newline

(A)

16 t+30 c=2,000

\newline

(B)

30 t+16 c=2,000

\newline

(C)

t+30 c=2,000

\newline

(D)

t+16 c=2,000

Define variables: Define the variables for the number of cars and trucks. $\newline$ Let $c$ represent the number of cars and $t$ represent the number of trucks.
Write equation based on gas tank volume: Write an equation based on the volume of gas tanks for cars and trucks. $\newline$ Each car has a gas tank of $16$ gallons, and each truck has a gas tank of $30$ gallons. The total volume of gas needed to fill all the tanks is $2,000$ gallons. $\newline$ The equation will be of the form: $16 \text{ gallons/car} \times \text{number of cars} + 30 \text{ gallons/truck} \times \text{number of trucks} = 2,000 \text{ gallons}.$
Translate information into mathematical equation: Translate the information into a mathematical equation. $\newline$ $16c + 30t = 2,000$
Match equation with given options: Match the equation with the given options. $\newline$ The equation we derived is $16c + 30t = 2,000$ , which matches option (B).

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