Using proportions, it is found that there were 12 pages in the program.
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
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, hence the proportion that the information about the actors took of the total number of pages x is given as follows:
[tex]\frac{1}{4} \times \left(1 - \frac{1}{3}\right)x = \frac{1}{4} \times \frac{2}{3}x = \frac{x}{6}[/tex]
This proportion is equivalent to the number of pages devoted to the authors, which was of 6, hence the total number is found as follows:
x/6 = 2
x = 12 pages.
There were 12 pages in the program.
More can be learned about proportions at https://brainly.com/question/24372153
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