You have $47 to spend on music and movie downloads. Each album download costs $7 and each movie download costs $8. Write and graph a linear inequality that represents this situation. Let x represent the number of albums and y the number of movies.
7 x + 8 y </= 47
To write a linear inequality that represents this situation, we need to consider the cost of the downloads in relation to the available budget.
Let's start by defining the variables:
x = the number of albums
y = the number of movies
Now let's consider the cost of the albums and movies:
Each album costs $7, so the total cost of the albums is 7x.
Each movie costs $8, so the total cost of the movies is 8y.
The total cost of the downloads can be represented as: 7x + 8y.
Since the available budget is $47, we can now write the inequality:
7x + 8y ≤ 47
This inequality represents that the total cost of the albums and movies should not exceed the available budget of $47.
To graph this inequality, we can rewrite the inequality in slope-intercept form:
8y ≤ -7x + 47
To graph this inequality, we can first plot the line y = -7x + 47. Then, since the inequality is inclusive (≤), we can shade the region below the line.
Here is a visual representation of the graph:
(0, 5.857)
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(-6.71, 0) __________|__________ (6.71, 0)
In this graph, any point below or on the line would represent a valid combination of albums and movies that can be purchased with the available budget.