Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Leslie works in the shipping department of a toy manufacturer. Toy cars weigh $5$ pounds apiece and are shipped in a container that weighs $6$ pounds when empty. Toy trucks, which weigh $1$ pound apiece, are shipped in a container weighing $18$ 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? $\newline$ Each container weighs $\_$ pounds and contains $\_$ toys.

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Solve a system of equations using substitution: word problems

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

\newline

Leslie works in the shipping department of a toy manufacturer. Toy cars weigh

5

pounds apiece and are shipped in a container that weighs

6

pounds when empty. Toy trucks, which weigh

1

pound apiece, are shipped in a container weighing

18

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?

\newline

Each container weighs

\_

pounds and contains

\_

toys.

Define Variables: Let's define two variables: let $x$ be the number of toy cars and $y$ be the number of toy trucks. We can write two equations based on the given information. The first equation will represent the total weight of the container with toy cars, and the second equation will represent the total weight of the container with toy trucks. Since both containers have the same weight when packed, we can set these two equations equal to each other.
Equation for 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 this is: $6 + 5x$ , where $6$ is the weight of the empty container and $5x$ is the weight of $x$ toy cars.
Equation for 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 this is: $18 + y$ , where $18$ is the weight of the empty container and $y$ is the weight of $y$ toy trucks.
Set Equations Equal: Since both containers have the same number of toys and the same weight, we can set the two equations equal to each other and also set $x$ equal to $y$ . This gives us the system of equations: $\newline$ $6 + 5x = 18 + y$ $\newline$ $x = y$
Substitute and Solve: Now we can use substitution to solve the system. Since $x = y$ , we can substitute $y$ for $x$ in the first equation: $6 + 5y = 18 + y$
Isolate y: Next, we solve for y by subtracting y from both sides of the equation: $\newline$ $6 + 5y - y = 18 + y - y$ $\newline$ $6 + 4y = 18$
Solve for y: Now we subtract $6$ from both sides to isolate the term with $y$ : $\newline$ $4y = 18 - 6$ $\newline$ $4y = 12$
Find $x$ : Divide both sides by $4$ to solve for $y$ :
$y = \frac{12}{4}$
$y = 3$
Final Toy Count: Since $x = y$ , $x$ is also equal to $3$ . Now we know there are $3$ toys in each container.
Calculate Container Weight: To find the weight of each container, we can substitute the value of $y$ back into either of the original equations. Let's use the first equation: $\newline$ $6 + 5x = 6 + 5(3) = 6 + 15 = 21$
Calculate Container Weight: To find the weight of each container, we can substitute the value of $y$ back into either of the original equations. Let's use the first equation: $6 + 5x = 6 + 5(3) = 6 + 15 = 21$ So each container weighs $21$ pounds and contains $3$ toys.