Question

active practice:
jason and laura are both downloading movies and songs from a new online company. jason purchases 6 movies and 4 songs and pays a total of $16.70. laura purchases 3 movies and 4 songs for $10.85. find the individual price of a movie and of a song.
ies cost choose your answer... and songs cost choose your answer... each to download.

Explanation:

Step1: Define variables

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

Step2: Set up equations

From Jason's purchase: \( 6m + 4s = 16.70 \)
From Laura's purchase: \( 3m + 4s = 10.85 \)

Step3: Subtract the second equation from the first

\( (6m + 4s) - (3m + 4s) = 16.70 - 10.85 \)
Simplify: \( 3m = 5.85 \)

Step4: Solve for \( m \)

\( m = \frac{5.85}{3} = 1.95 \)

Step5: Substitute \( m = 1.95 \) into the second equation

\( 3(1.95) + 4s = 10.85 \)
Calculate: \( 5.85 + 4s = 10.85 \)
Subtract 5.85: \( 4s = 10.85 - 5.85 = 5 \)

Step6: Solve for \( s \)

\( s = \frac{5}{4} = 1.25 \)

Answer:

A movie costs $1.95 and a song costs $1.25.