Question

write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.
emmett received some gift cards for music and movie downloads for his birthday. using one of them, he downloaded 18 songs and 13 movies, which cost a total of $148. using another, he purchased 6 songs and 14 movies, which cost a total of $146. how much does each download cost?
downloads cost $\boxed{}$ for a song and $\boxed{}$ for a movie.

Explanation:

Step1: Define Variables

Let \( s \) be the cost of a song download (in dollars) and \( m \) be the cost of a movie download (in dollars).

Step2: Set Up Equations

From the first purchase: \( 18s + 13m = 148 \)
From the second purchase: \( 6s + 14m = 146 \)

Step3: Eliminate \( s \)

Multiply the second equation by 3: \( 18s + 42m = 438 \)
Subtract the first equation:
\( (18s + 42m) - (18s + 13m) = 438 - 148 \)
\( 29m = 290 \)
\( m = 10 \)

Step4: Solve for \( s \)

Substitute \( m = 10 \) into \( 6s + 14m = 146 \):
\( 6s + 14(10) = 146 \)
\( 6s + 140 = 146 \)
\( 6s = 6 \)
\( s = 1 \)

Answer:

A song download costs $1 and a movie download costs $10. So the blanks are filled with 1 (for a song) and 10 (for a movie).