Help with problem please

Question

Dustin works in the shipping department of a toy manufacturer. Toy cars weigh 2 pounds apiece and are shipped in a container that weighs 13 pounds when empty. Toy trucks, which weigh 1 pound apiece, are shipped in a container weighing 17 pounds. When packed with toys and ready for shipment, both kinds of containers have the same number of toys and the same weight. What is the weight of each container? What is the number of toys?

Answer 1

These word problems are really simple once you understand how to put them into an equation. Always look for the clues in the problem. We have Car = 2 lbs, car crate = 13 lbs. Truck = 1 lb, truck crate = 17 lbs.

Since the number of toys in each box are equal, we can let x = number of toys.

If there are 10 cars in a box, the weight of the cars alone is 10*2lbs or 20 lbs. Adding the weight of the crate, 13, gives us a total weight of 20 + 13 = 33. However, If there are 5 cars, it's 5*2 or 10 lbs + 13 = 23 lbs. So if there are x cars in a box, it's x*2 or simply 2x lbs. Adding the weight of the crate we have (2x + 13) lbs.

Similarly, each truck weighs 1 lb. There are the same number of trucks in a box as there are cars in a box, so we have 1x lbs for the weight of the trucks, plus the weight of the crate for trucks, 17 lbs, giving us (1x+17) lbs.

Since the crates, when full, weigh the same, we can now say (2x + 13) = (1x + 17). From here, we solve for x.

We need to get x to one side and the other numbers to the other side. So if we subtract 1x from both sides we get (2x - 1x) + 13 = 17. Now subtract 13 from both sides to get the x variables alone, so we have (2x - 1x) = (17 - 13). This reduces to x = 4. So the number of toys in each box is 4. We can verify that by plugging 4 into each equation.

2(4) + 13 = 8 + 13 = 21.

1(4) + 17 = 4 + 17 = 21.

So we have verified that there are 4 toys in each crate, and that each crate weighs 21 lbs.