or
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Valeria received some gift cards for music and movie downloads for her birthday. Using one of them, she downloaded 7 songs and 12 movies, which cost a total of $170. Using another, she purchased 12 songs and 12 movies, which cost a total of $180. How much does each download cost?
Downloads cost $
for a song and $
for a movie.
Let x be the cost of a music download and y be the cost of a movie download.
From the given information, we can write the following system of equations:
7x + 12y = 170
12x + 12y = 180
Now we can solve this system using any method, such as substitution or elimination.
Using the substitution method:
From the first equation, we can express x in terms of y:
x = (170 - 12y)/7
Substituting this expression for x into the second equation:
12((170 - 12y)/7) + 12y = 180
Multiplying both sides of the equation by 7 to eliminate the denominator:
12(170 - 12y) + 84y = 1260
2040 - 144y + 84y = 1260
-60y = -780
y = 13
Substituting this value of y back into the first equation:
7x + 12(13) = 170
7x + 156 = 170
7x = 14
x = 2
So, a music download costs $2 and a movie download costs $13.