Question

last month yolanda downloaded 3 games and 2 audiobooks on her tablet for a total of $16.
this month she downloaded 5 games and 6 audiobooks on her tablet for a total of $42.
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.
□x + □y = □
□x + □y = □
(b) how much did it cost (in dollars) to download each game and each audiobook?
cost for each game: $□
cost for each audiobook: $□

Explanation:

Part (a)

Step1: Analyze last month's cost

Last month, 3 games (cost \(3x\)) and 2 audiobooks (cost \(2y\)) totaled $16. So, \(3x + 2y = 16\).

Step2: Analyze this month's cost

This month, 5 games (cost \(5x\)) and 6 audiobooks (cost \(6y\)) totaled $42. So, \(5x + 6y = 42\).

Part (b)

Step1: Multiply first equation

Multiply \(3x + 2y = 16\) by 3: \(9x + 6y = 48\).

Step2: Subtract second equation

Subtract \(5x + 6y = 42\) from \(9x + 6y = 48\):
\((9x - 5x)+(6y - 6y)=48 - 42\)
\(4x = 6\)
\(x=\frac{6}{4}=1.5\).

Step3: Substitute x into first equation

Substitute \(x = 1.5\) into \(3x + 2y = 16\):
\(3(1.5)+2y = 16\)
\(4.5 + 2y = 16\)
\(2y = 16 - 4.5 = 11.5\)
\(y=\frac{11.5}{2}=5.75\).

Answer:

s:
(a) The system is:
\(3x + 2y = 16\)
\(5x + 6y = 42\)

(b) Cost for each game: $\(1.5\)
Cost for each audiobook: $\(5.75\)