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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Vicky works in the shipping department of a toy manufacturer. Toy cars weigh pounds apiece and are shipped in a container that weighs pounds when empty. Toy trucks, which weigh pounds apiece, are shipped in a container weighing 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?Each container weighs pounds and contains toys.
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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Vicky works in the shipping department of a toy manufacturer. Toy cars weigh pounds apiece and are shipped in a container that weighs pounds when empty. Toy trucks, which weigh pounds apiece, are shipped in a container weighing 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?Each container weighs pounds and contains toys.
- Denote number of toys: Let's denote the number of toy cars as and the number of toy trucks as . According to the problem, both kinds of containers have the same number of toys, so we have:
- Calculate weight of toy cars: The weight of the container with toy cars is the weight of the empty container plus the weight of the toy cars. The equation for the container with toy cars is:Weight of toy cars container =
- Calculate weight of toy trucks: Similarly, the weight of the container with toy trucks is the weight of the empty container plus the weight of the toy trucks. The equation for the container with toy trucks is:Weight of toy trucks container =
- Set equations equal: Since both containers weigh the same when packed with toys, we can set the two equations equal to each other:
- Substitute and simplify: We already know that from Step , so we can substitute for in the equation from Step :
- Solve for x: Now we solve for x. First, we'll subtract from both sides to get the x terms on one side:
- Isolate x term: Next, we'll subtract from both sides to isolate the term with :
- Find x value: Finally, we divide both sides by to solve for x:
- Determine value: Since , we also have:
- Calculate weight of toy cars: Now that we know the number of toys and , we can find the weight of each container. For the toy cars container:Weight of toy cars container = pounds
- Calculate weight of toy trucks: For the toy trucks container:Weight of toy trucks container = pounds
