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tino4ka555 [31]
2 years ago
7

A video store specializes in three types of movies: children's, American West, and horror. It's known that:

Mathematics
1 answer:
xenn [34]2 years ago
6 0

X, y, z denote children's movies, western movies, and horror movies, respectively. The related system of equations is formed and solved.

\left\{\begin{matrix} \qquad\qquad\ \dfrac{60}{100}x + \dfrac{50}{100}y =\dfrac{30}{100}(x+y+z)\\ \dfrac{20}{100}x+ \dfrac{60}{100}y+ \dfrac{60}{100}z= \dfrac{1}{2}(x+y+z) \\ \ \ \ x+100=y \end{matrix} \right.\

Simplifying the system of equations, we have

\left\{\begin{matrix} 3x + 2y -3z=0\\ -3x+ y+ z= 0 \\ \ \ \ x+100=y \end{matrix} \right.\ \ \Longrightarrow \ \left\{\begin{matrix} 5x-3z=-200\\ -2x+ z= -100 \end{matrix} \right.\

\ \ \  5x-3z=-200\\\underline{-6x+3z=-300} \ \Rightarrow \ x=500\\\ \ -x+0= \ 500

                                       y&=500+100=600\\ z&=3(500)-600=900

The video store has 500 children's movies, 600 westerns and 900 horror movies.

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