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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

Nayeli is proofreading a 7575 page manuscript. Fil\u0000e99mon is line editing a 4040 page manuscript.\newlineSince proofreading is faster, Nayeli completes 1111 pages an hour, but Fil\u0000e99mon only completes 44 pages an hour.\newlineWhen Nayeli and Fil\u0000e99mon have the same number of pages left, how many pages will that be?\newlinepages

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Full solution

Q. Nayeli is proofreading a 7575 page manuscript. Fil\u0000e99mon is line editing a 4040 page manuscript.\newlineSince proofreading is faster, Nayeli completes 1111 pages an hour, but Fil\u0000e99mon only completes 44 pages an hour.\newlineWhen Nayeli and Fil\u0000e99mon have the same number of pages left, how many pages will that be?\newlinepages
  1. Determine Rates: Determine the rate at which Nayeli and Filémon are completing their tasks.\newlineNayeli's rate = 1111 pages per hour\newlineFilémon's rate = 44 pages per hour
  2. Set Up Equation: Set up an equation to find out after how many hours they will have the same number of pages left.\newlineLet xx be the number of hours they both work until they have the same number of pages left.\newlineNayeli's remaining pages = Total pages - Pages completed by Nayeli\newlineNayeli's remaining pages = 75−11x75 - 11x\newlineFilémon's remaining pages = Total pages - Pages completed by Filémon\newlineFilémon's remaining pages = 40−4x40 - 4x
  3. Solve Equation: Since they have the same number of pages left after xx hours, we can set the expressions for their remaining pages equal to each other.75−11x=40−4x75 - 11x = 40 - 4x
  4. Find Pages Left: Solve the equation for xx.75−11x=40−4x75 - 11x = 40 - 4xAdd 11x11x to both sides:75=40+7x75 = 40 + 7xSubtract 4040 from both sides:35=7x35 = 7xDivide both sides by 77:x=5x = 5
  5. Substitute Value: Determine the number of pages left after xx hours.\newlineSince x=5x = 5, we can substitute this value into the expression for Nayeli's remaining pages or Filémon's remaining pages.\newlineNayeli's remaining pages = 75−11(5)=75−55=2075 - 11(5) = 75 - 55 = 20\newlineFilémon's remaining pages = 40−4(5)=40−20=2040 - 4(5) = 40 - 20 = 20

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