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Rafael, Denise, and Philippe are doing a project together. They decide to base the project on a book that is 540 pages long. Rafael plans to read a certain number of pages. Denise will read Three-fourths of the number of pages Rafael reads, and Philippe will read One-half of the number of pages that Rafael reads. How many pages will Rafael read?

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Rafael will read 240 pages.

Step-by-step explanation:

Let's start by setting up the unknowns:

x = # of Rafael's pages

x/2 = # of Philippe's pages

(3/4)x = # of Denise's pages

Set these all equal to 540:

(x) + (x / 2) + (3/4(x)) = 540

Let's multiply both sides by 4 to make this easier.

4x + 2x + 3x = 2160

9x = 2160

x = 240

x was the # of Rafael's pages, so Rafael will read 240 pages. This means that Philippe will read 120 pages (one-half of Rafael), and Denise will read 180 pages (three-fourths of Rafael). Adding these all up will get you 540 pages, so it checks out.

Hope this helps!
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