Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

Question

Norma works in the shipping department of a toy manufacturer. Toy cars weigh 1 kilogram apiece and are shipped in a container that weighs 10 kilograms when empty. Toy trucks, which weigh 5 kilograms apiece, are shipped in a container weighing 2 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? What is the number of toys?

Each container weighs
kilograms and contains
toys.

Answer 1

Let's denote:

• \( x \): the number of toy cars.
• \( y \): the number of toy trucks.

From the problem statement, we have the following information:

1. Each toy car weighs 1 kg, and the empty container for toy cars weighs 10 kg. Thus, the total weight of the container with toy cars is \( 10 + x \) kg.
2. Each toy truck weighs 5 kg, and the empty container for toy trucks weighs 2 kg. Thus, the total weight of the container with toy trucks is \( 2 + 5y \) kg.
3. The problem states that both containers have the same weight and contain the same number of toys, which gives us the equations:

\[ 10 + x = 2 + 5y \quad \text{(1)} \] \[ x = y \quad \text{(2)} \]

Now, we can substitute equation (2) into equation (1):

From (2), we have \( y = x \). Substitute \( y \) in equation (1):

\[ 10 + x = 2 + 5x \]

Now, solve for \( x \):

\[ 10 + x - 5x = 2 \] \[ 10 - 4x = 2 \] \[ -4x = 2 - 10 \] \[ -4x = -8 \] \[ x = 2 \]

Now, using equation (2) to find \( y \):

\[ y = x = 2 \]

Now we can find the weight of each container. For toy cars:

Weight of toy cars' container: \[ 10 + x = 10 + 2 = 12 \text{ kg} \]

For toy trucks:

Weight of toy trucks' container: \[ 2 + 5y = 2 + 5 \cdot 2 = 2 + 10 = 12 \text{ kg} \]

Hence, both containers weigh the same.

Thus, the final answers are:

Each container weighs 12 kilograms and contains 2 toys.