Information about a play took up 1/3 of the pages in the program. Information about the actors took up 1/4 of the remaining pages. Information about the director, the producer, and the designer took up 2 pages, the same number of pages devoted to actors how many pages were there in the program?
(1/3)x + (1/4)(2/3)x + 2 = x
solve for x
x - (1/3)x - (1/6)x = 2
(6x - 2x - x)/6 = 2
3x/6 = 2
x=4 ans.
To find the total number of pages in the program, we will use a step-by-step approach.
Step 1: Let's assume the total number of pages in the program is "x".
Step 2: According to the information given, the play took up 1/3 of the pages in the program. So, the number of pages dedicated to the play is (1/3) * x.
Step 3: After the play, the remaining pages in the program would be (x - (1/3) * x), which simplifies to (2/3) * x.
Step 4: The information about the actors took up 1/4 of the remaining pages. So, the number of pages dedicated to the actors is (1/4) * (2/3) * x.
Step 5: The information about the director, producer, and designer took up 2 pages, the same number of pages devoted to actors. Therefore, (1/4) * (2/3) * x = 2.
Step 6: To solve for x, we need to isolate it on one side of the equation. Multiply both sides of the equation by (4/2)*(3/1) = 12.
(1/4) * (2/3) * x * 12 = 2 * 12
Simplifying, we get:
(2/3) * x * 4 = 24
8/3 * x = 24
Step 7: Multiply both sides of the equation by (3/8) to isolate x.
(8/3 * x) * (3/8) = (24) * (3/8)
x = 9
Therefore, there were 9 pages in the program.