Question

FREIGHT TRAINS A train with 150 freight cars is used to haul two types of grain. Each freight car can haul 97.3 tons of barley or 114 tons of corn. Let \(n\) represent the number of freight cars containing corn. If 90 freight cars contain corn, what is the total weight the train is hauling?

Short answer

The total weight the train is hauling is 16098 tons.

Step-by-step solution

Determine the number of corn freight cars

According to the problem, there are 90 freight cars containing corn.

Weight of corn freight cars

Knowing that each freight car of corn hauls 114 tons, the total weight hauled by the corn freight cars is found by multiplying the number of cars by the weight each car can carry: \(90 \times 114 = 10260\) tons.

Determine the number of barley freight cars

The train is made up of 150 freight cars in total. Subtracting the 90 freight cars that carry corn leaves 60 freight cars to carry barley.

Weight of barley freight cars

Each freight car of barley hauls 97.3 tons so the total weight hauled by the barley freight cars is \(60 \times 97.3 = 5838\) tons.

Total weight hauled by the train

The total weight hauled by the train is found by adding up the weights carried by the corn and barley freight cars: \(10260 + 5838 = 16098\) tons.