Question

(1) he saw twice as many 1.5 h space movies as he did 2 h mysteries. (2) he spent a total of 15 h watching movies. chart: columns \space movies\, \mystery movies\; rows \movie length × number of movies = total time\, with \?\ in cells.

Explanation:

Step1: Define variables

Let the number of mystery movies be \( x \), and the length of each mystery movie be \( 2 \) h (from "twice as many 1.5 h space movies as he did 2 h mysteries" – wait, re - read: "He saw twice as many 1.5 h space movies as he did 2 h mysteries. He spent a total of 15 h watching movies." So let the number of mystery movies be \( n \), then the number of space movies is \( 2n \). The length of each mystery movie is \( 2 \) h, and the length of each space movie is \( 1.5 \) h.

Step2: Set up the equation

The total time is the sum of the time spent on space movies and mystery movies. The time for space movies is \( 1.5\times(2n) \), and the time for mystery movies is \( 2\times n \). So the equation is \( 1.5\times(2n)+2\times n = 15 \).

Simplify the left - hand side: \( 3n + 2n=15 \), which is \( 5n = 15 \).

Step3: Solve for \( n \)

Divide both sides of the equation \( 5n = 15 \) by \( 5 \): \( n=\frac{15}{5}=3 \).

So the number of mystery movies is \( n = 3 \), and the number of space movies is \( 2n=6 \).

The time for space movies: \( 1.5\times6 = 9 \) h, and the time for mystery movies: \( 2\times3 = 6 \) h.

Filling the table:

	Space movies	Mystery movies
Number of movies	\( 6 \)	\( 3 \)
Total time	\( 9 \) h	\( 6 \) h

Answer:

• Number of space movies: \( 6 \), Time for space movies: \( 9 \) h
• Number of mystery movies: \( 3 \), Time for mystery movies: \( 6 \) h

(And the table is filled as above)