One Problem at a Time

Linear Equations Application

Problem 198: A class used cars and buses for a field trip. They used 6 vehicles for this trip. Each cars hold 5 students and each bus holds 30 students. If 80 students went to the trip how many of each vehicle did they use?

Solution: Let x be the amount of cars used and y the amount of buses used. That is, we have x + y = 6 so that y = 6 -x. Hence,

(1)   \begin{align*}  5x + 30y & = 80 \\ 5x + 30 (6-x) & = 80 \\ 5x + 180 - 30 x & = 80 \\ -25x + 180 & = 80 \\ -25x & = -100 \\ x & = 4.\end{align*}

Now that we know x we can find y. Thus

(2)   \begin{align*} y & = 6 - x \\  & = 6 -4 \\ & = 2. \end{align*}

Therefore, they used 4 cars and 2 buses for the trip.

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