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saul85 [17]
3 years ago
12

The scale on a map is stated as 1:100000. On the map, Jennifer estimates that the distance to her destination is 8cm. If she is

correct in her estimate, how many kilometres is it to her destination?
Mathematics
1 answer:
Gnoma [55]3 years ago
3 0

Answer:

8km

Step-by-step explanation:

1:100,000 = 1.6 miles = 1 kilometer x 8 = 8 km

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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

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

6 0
2 years ago
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Answer:

Step-by-step explanation:

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