To find: To write a matrix equation describing the purchase. To solve the matrix equation to find the price of a movie and the price of a video game.
Each movie costs $9.50 and each video game costs $12.50
Given information:
Given, a local store is having a special promotion where all movies sell at the same price and all video games sell at another price. 5 movies and 4 video games cost $97.50 and 3 movies and 6 video games cost $103.50.
Calculation:
Let each movie cost x and each video game cost y.
So the cost of 5 movies and 4 video games is given by
The cost of 3 movies and 6 video games is given by
The matrix equation is given by:
Multiplying both sides by the inverse of the matrix on the left gives the required solution.
The determinant of the matrix is given by:
Since the determinant is not 0, the inverse exists.
The inverse of a 2X2 matrix
Plugging the values, the inverse matrix is given by:
Multiplying both sides of the equation by the inverse:
Hence,
Conclusion:
Each movie costs $9.50 and each video game costs $12.50
Chapter 12 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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