math
posted by Jane on .
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.

each album costs $7 and you buy x of them
cost of albums = 7x
each movie costs $8 and you have you have y of them
cost of movies = 8y
total cost is has to be less than $47
> 7x + 8y < 47
sketch the graph of 7x + 8y = 47 , a straight line, and shade in the region below that line. Of course you would stay in the first quadrant, (x > 0, and y >0 , since you can't have negative number of movies and albums)
Since you can't buy partial albums and movies, both x and y have to be whole numbers.
So for solutions you would consider only ordered pairs that have whole numbers as their components.
e.g. (2, 2) or (1,5)