Question

You have prizes to rewAlgebra 10.9 Solve a system of equations using substitution: Word problems US9Write a system of equations to describe the situation below, solve using substitution, and fillin the blanks.Nicole works in the shipping department of a toy manufacturer. Toy cars weigh 3 poundsapiece and are shipped in a container that weighs 4 pounds when empty. Toy trucks, whichweigh 1 pound apiece, are shipped in a container weighing 10 pounds. When packed withtoys and ready for shipment, both kinds of containers have the same number of toys and thesame weight. What is the weight of each container? What is the number of toys?

Answer 1

The weight of each container is 13 pounds and the number of toys is 3.

Step-by-step explanation:

If y is the weight of each container and x is the number of toys, we get that the system of equations is

y = 3x + 4

y = 1x + 10

Because the weight of a container of toy cars is equal to 3 pounds times the number of toy cars added to 4 pounds when the container is empty. In the same way, the weight of a container of toy trucks is equal to 1 pound times the number of toy trucks added to 10 pounds when the container is empty.

Now, we can solve the expression using subtitution. Replacing the first equation on the second equation, we get

y = x +10

3x + 4 = x + 10

Then, solve for x as follows

3x + 4 - 4 = x + 10 - 4

3x = x + 6

3x - x = x + 6 - x

2x = 6

2x/2 = 6/2

x = 3

With the value of x, we can calculate y as

y = 3x + 4

y = 3(3) + 4

y = 9 + 4

y = 13

Therefore, the weight of each container is 13 pounds and the number of toys is 3.