A company sells three types of gift baskets. The basic basket has two movie passes and one package of microwave popcorn, and costs $15.50. The medium basket has two movie passes, two packages of microwave popcorn, and one DVD, and costs $37. The super basket has four movie passes, three packages of microwave popcorn, and two DVDs, and costs $72.50.



Create a system of equations and solve using matrices to find the price of each basket item.

The price of each movie is $7, the price of each microwave popcorn is $1.50 and the price of each DVD is $20.

Let x represent the cost of each movie, y represent the cost each microwave and z represent the cost of each DVD.

For the basic:

2x + y = 15.50    (1)

For medium:

2x + 2y + z = 37    (2)

For super:

4x + 3y + 2z = 72.50  (3)

[tex]\left[\begin{array}{ccc}2&1&0\\2&2&1\\4&3&2\end{array}\right] \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}15.5&37&72.5\end{array}\right] \\\\\\ \left[\begin{array}{c}x&y&z\end{array}\right] =\left[\begin{array}{ccc}2&1&0\\2&2&1\\4&3&2\end{array}\right]^{-1}\left[\begin{array}{c}15.5&37&72.5\end{array}\right]\\\\\\ \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}7&1.5&20\end{array}\right] =[/tex]

The price of each movie is $7, the price of each microwave popcorn is $1.50 and the price of each DVD is $20.

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