Question

Carly works in the shipping department of a toy manufacturer. Toy cars weigh 1 kilogram apiece and are shipped in a container that weighs 7 kilograms when empty. Toy trucks, which weigh 2 kilograms apiece, are shipped in a container weighing 5 kilograms. 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?

Answer 1

9 kg

Explanation:

The toys have a difference in mass of 1 kg; the containers have a difference in mass of 2 kg, so it only takes 2 toys per container to make up the difference in container mass.

2 cars @ 1 kg ea + 7 kg container = 9 kg

2 trucks @ 2 kg ea + 5 kg container = 9 kg

The containers ready for shipment have a mass of 9 kg.

Answer 2

9 kg

Explanation:

1. Let x be the number of car toys packed into container. Toy cars weigh 1 kilogram apiece and are shipped in a container that weighs 7 kilograms when empty, then the total weight of container with toy cars is

`x\cdot 1+7=x+7\ kg.`

2. The number of toy trucks is also x. Toy trucks, which weigh 2 kilograms apiece, are shipped in a container weighing 5 kilograms, then the total weight of container with toy trucks is

`x\cdot 2+5=2x+5\ kg.`

3. When packed with toys and ready for shipment, both kinds of containers have the same weight. Thus,

`x+7=2x+5,\\ \\7-5=2x-x,\\ \\2=x,\\ \\x=2.`

4. The weight of each container is
`2+7=9\ kg.`