Question

2/5Solving a word problem using a system oflinear equations of the form Ax + By = C

Answer 1

Let's set x for each movie

Set y for each video.

Now, we have the next given information:

One month Latoya rented 2 movies and 3 video games.

We can write the next equation:

2x + 3y = 19

Also, the next she rented 4 movies and 8 video games.

We can write the next equation:

4x + 8y = 49

With both equations with the same variables, we have a system of equations:

1) 2x + 3y = 19

2) 4x + 8y = 49

Solve the system of equations using the elimination method.

First, multiply the first function by 4 and then multiply the second function by 2.

4(2x + 3y = 19)

8x +12y =76

and

2(4x + 8y = 49)

8x + 16y = 98

Subtract both functions:

`\begin{gathered} 8x+12y=76 \\ 8x+16y=98 \\ --------------- \\ (8x-8x)+(12y-16y)=(76-98) \\ 0-4y=-22 \\ \text{Solve for y:} \\ y=(-22)/(-4) \\ y=5.5 \end{gathered}`

With the y value, we can replace it on the first function:

`\begin{gathered} 2x+3y=19 \\ 2x+3(5.5)=19 \\ \text{Solve for x:} \\ 2x+16.5=19 \\ 2x=2.5 \\ x=(2.5)/(2) \\ x=1.25 \end{gathered}`

Hence:

The rental cost for each movie is $1.25

The rental cost for each video game is $5.5