Question

last month linda downloaded 3 games and 5 audiobooks on her tablet for a total of $30. this month she downloaded 6 games and 2 audiobooks on her tablet for a total of $18. each game costs the same, and each audiobook costs the same. let x be the cost (in dollars) of downloading a game. let y be the cost (in dollars) of downloading an audiobook. (a) write a system of equations that could be used to find the cost (in dollars) for each game and each audiobook. \\(\square x + \square y = \square\\) \\(\square x + \square y = \square\\) (b) how much did it cost (in dollars) to download each game and each audiobook? cost for each game: $\square$ cost for each audiobook: $\square$

Explanation:

Part (a)

Step1: Form first equation

Last month, 3 games (cost \(3x\)) and 5 audiobooks (cost \(5y\)) total $30. So equation: \(3x + 5y = 30\)

Step2: Form second equation

This month, 6 games (cost \(6x\)) and 2 audiobooks (cost \(2y\)) total $18. So equation: \(6x + 2y = 18\)

Part (b)

Step1: Simplify second equation

Divide \(6x + 2y = 18\) by 2: \(3x + y = 9\) → \(y = 9 - 3x\)

Step2: Substitute \(y\) into first equation

Substitute \(y = 9 - 3x\) into \(3x + 5y = 30\):
\(3x + 5(9 - 3x) = 30\)
\(3x + 45 - 15x = 30\)
\(-12x = -15\)
\(x = \frac{15}{12} = 1.25\)

Step3: Find \(y\)

Substitute \(x = 1.25\) into \(y = 9 - 3x\):
\(y = 9 - 3(1.25) = 9 - 3.75 = 5.25\)

Answer:

s:
(a) \(3x + 5y = 30\)
\(6x + 2y = 18\)

(b) Cost for each game: $\(1.25\)
Cost for each audiobook: $\(5.25\)