Question

last month bob downloaded 6 games and 2 audiobooks on his tablet for a total of $24. this month he downloaded 3 games and 5 audiobooks on his tablet for a total of $33. 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. \boxed{}x + \boxed{}y = \boxed{} \boxed{}x + \boxed{}y = \boxed{} (b) how much did it cost (in dollars) to download each game and each audiobook? cost for each game: $\boxed{} cost for each audiobook: $\boxed{}

Explanation:

Part (a)

Step1: Analyze last month's cost

Last month, Bob downloaded 6 games (cost \(6x\)) and 2 audiobooks (cost \(2y\)) for a total of $24. So the first equation is \(6x + 2y = 24\).

Step2: Analyze this month's cost

This month, he downloaded 3 games (cost \(3x\)) and 5 audiobooks (cost \(5y\)) for a total of $33. So the second equation is \(3x + 5y = 33\).

Step1: Simplify the first equation

Divide the first equation \(6x + 2y = 24\) by 2: \(3x + y = 12\). Then, solve for \(y\): \(y = 12 - 3x\).

Step2: Substitute \(y\) into the second equation

Substitute \(y = 12 - 3x\) into \(3x + 5y = 33\):
\(3x + 5(12 - 3x) = 33\)
\(3x + 60 - 15x = 33\)
\(-12x = 33 - 60\)
\(-12x = -27\)
\(x = \frac{-27}{-12} = 2.25\)

Step3: Find \(y\)

Substitute \(x = 2.25\) into \(y = 12 - 3x\):
\(y = 12 - 3(2.25) = 12 - 6.75 = 5.25\)

Answer:

\(6x + 2y = 24\)
\(3x + 5y = 33\)

Part (b)