A shipment of 18 cars, some weighing 3,000 pounds, and the others weighing 5,000 pounds each. Together the shipment has a total weight of 30 tons. (60,000 lbs). Find the number of each kind of car.

The best way to solve a problem like this is to set up two equations. First assign a variable to each thing you are trying to find. In this case, it’s two different kinds of cars. Let’s call the cars that weigh 3,000 pounds x, and the ones that weigh 5,000 y. The two equations you should write are:

x+y=18 (because the problem tells you there were 18 cars in total)
3000x+5000y=60000 (because that is the total weight in the problem)

Next, you need to solve for one of the variables. I will solve for x first by subtracting y from both sides of the first equation.

x=18-y

Then you have to plug that into the other equation to get:

3000(18-y)+5000y=60000

Simplify and solve for y:

54000-3000y+5000y=60000
54000+2000y=60000
2000y=6000
y=3

Now that you know what y equals, you can put it into the equation we solved for x:

x=18-3
x=15

So there are 15 cars that weigh 3000 pounds and 3 that weigh 5000.

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