Question

Sammi borrowed 11 DVDs from her local library for a total of 1,200 minutes. All of the DVDs were either animated or a superhero movie. Each of the animated DVDs lasted for about 90 minutes. Each superhero movies lasted about 120 minutes. How many of each type of movie did Sammi borrow?

In your handwritten work do the following:

Clearly define your variables used
Write a system of linear equations representing the scenario
Solve the system of equations algebraically either by substitution or elimination
Check your solution algebraically and describe what your solution means in context
In the textbox below:

Write your solution and describe why you chose the method you did (substitution or elimination) instead of choosing the other option. After solving, do you feel you chose the most efficient or easiest method?

Answer 1

Let x be the number of animated DVDs Sammi borrowed and y be the number of superhero DVDs she borrowed.

The total number of minutes of all DVDs is 1,200, so we have:

90x + 120y = 1,200

And the total number of DVDs borrowed is 11, so we have:

x + y = 11

To solve this system of linear equations, we can use substitution method. Solving for y in the second equation, we get:

y = 11 - x

Substituting this expression for y into the first equation, we have:

90x + 120(11 - x) = 1,200

Expanding the right side, we get:

90x + 1320 - 120x = 1,200

Combining like terms, we get:

-30x = -120

Solving for x, we get:

x = 4

Since x is the number of animated DVDs, Sammi borrowed 4 animated DVDs. Substituting this value of x back into the expression for y, we have:

y = 11 - x = 11 - 4 = 7

So Sammi borrowed 7 superhero DVDs.

The solution means that Sammi borrowed 4 animated DVDs and 7 superhero DVDs, which lasted for a total of 1,200 minutes. This method was relatively simple and efficient, as it only involved solving for one variable and then using substitution.