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Cory, Josh and Dan went shopping for Halloween treats. Cory bought 3 chocolate pumpkins, 4 masks and 8 candy witches. He spent $41.63. Josh bought 6 chocolate pumpkins, 2 masks and 14 candy witches. He spent $45.52. Dan bought 8 chocolate pumpkins, 3 masks and 25 candy witches. He spent $72.87. Write a system of equations to represent this problem and perform a matrix calculation to determine the unit price of each item purchased. Enter your answer according to this example with dollar signs and no spaces for the price of the chocolate pumpkin, mask, and candy witch respectively: ($3.29,$8.65,$2.47) *

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Answer:

The cost of chocolate pumpkins is $1.89, masks cost $5.75 and candy witches cost $1.62

Step-by-step explanation:

Let x represent the cost of chocolate pumpkins, y the cost of masks and z the cost of candy witches.

Cory shopping can be represented as:

3x + 4y + 8z = 41.63      (1)

Josh shopping can be represented as:

6x + 2y + 14z = 45.52    (2)

Dan shopping can be represented as:

8x + 3y + 25z = 72.87    (3)

The equations in matrix form is:

[tex]\left[\begin{array}{ccc}3&4&8\\6&2&14\\8&3&25\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}41.63\\45.52\\72.87\end{array}\right] \\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}3&4&8\\6&2&14\\8&3&25\end{array}\right] ^{-1}\left[\begin{array}{c}41.63\\45.52\\72.87\end{array}\right] \\\\\\\left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{c}1.89\\5.75\\1.62\end{array}\right][/tex]

The cost of chocolate pumpkins is $1.89, masks cost $5.75 and candy witches cost $1.62