Nayeli is proofreading a 75 page manuscript. Filémon is line editing a 40 page manuscript. Since proofreading is faster, Nayeli completes 11 pages an hour, but Filémon only completes 4 pages an hour. When Nayeli and Filémon have the same number of pages left, how many pages will that be? pages

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Determine Rates: Determine the rate at which Nayeli and Filémon are completing their tasks. Nayeli's rate = 11 pages per hour Filémon's rate = 4 pages per hourSet Up Equation: Set up an equation to find out after how many hours they will have the same number of pages left. Let x be the number of hours they both work until they have the same number of pages left. Nayeli's remaining pages = Total pages - Pages completed by Nayeli Nayeli's remaining pages = 75 - 11x Filémon's remaining pages = Total pages - Pages completed by Filémon Filémon's remaining pages = 40 - 4xSolve Equation: Since they have the same number of pages left after x hours, we can set the expressions for their remaining pages equal to each other. 75 - 11x = 40 - 4xFind Pages Left: Solve the equation for x. 75 - 11x = 40 - 4x Add 11x to both sides: 75 = 40 + 7x Subtract 40 from both sides: 35 = 7x Divide both sides by 7: x = 5Substitute Value: Determine the number of pages left after x hours. Since x = 5, we can substitute this value into the expression for Nayeli's remaining pages or Filémon's remaining pages. Nayeli's remaining pages = 75 - 11(5) = 75 - 55 = 20 Filémon's remaining pages = 40 - 4(5) = 40 - 20 = 20

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