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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineLast Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Maya can read 22 pages per minute, and she had already read 8787 pages. Ariel, who has a reading speed of 44 pages per minute, had read 99 pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?\newlineAfter __\_\_ minutes, Maya and Ariel had each read __\_\_ pages.

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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.\newlineLast Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Maya can read 22 pages per minute, and she had already read 8787 pages. Ariel, who has a reading speed of 44 pages per minute, had read 99 pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?\newlineAfter __\_\_ minutes, Maya and Ariel had each read __\_\_ pages.
  1. Define Variables: Let's define the variables:\newlineLet tt be the time in minutes after they started reading at the same time.\newlineLet PmP_m be the total number of pages Maya has read after tt minutes.\newlineLet PaP_a be the total number of pages Ariel has read after tt minutes.\newlineWe can write two equations to represent the situation:\newlineFor Maya: Pm=87+2tP_m = 87 + 2t (since she reads 22 pages per minute and had already read 8787 pages).\newlineFor Ariel: Pa=9+4tP_a = 9 + 4t (since she reads 44 pages per minute and had already read PmP_m00 pages).\newlineWe want to find the value of tt when PmP_m22.
  2. Set Up Equations: Now we set up the system of equations:\newline11) Pm=87+2tP_m = 87 + 2t\newline22) Pa=9+4tP_a = 9 + 4t\newlineSince Pm=PaP_m = P_a, we can equate the two expressions:\newline87+2t=9+4t87 + 2t = 9 + 4t
  3. Solve for t: Next, we solve for t using substitution:\newlineSubtract 2t2t from both sides of the equation:\newline87+2t−2t=9+4t−2t87 + 2t - 2t = 9 + 4t - 2t\newlineThis simplifies to:\newline87=9+2t87 = 9 + 2t
  4. Substitute and Solve: Now, subtract 99 from both sides of the equation:\newline87−9=9+2t−987 - 9 = 9 + 2t - 9\newlineThis simplifies to:\newline78=2t78 = 2t
  5. Find Pages Read: Divide both sides by 22 to solve for tt:782=2t2\frac{78}{2} = \frac{2t}{2}This gives us:t=39t = 39
  6. Find Pages Read: Divide both sides by 22 to solve for tt:782=2t2\frac{78}{2} = \frac{2t}{2}This gives us:t=39t = 39Now that we have the value of tt, we can find out how many pages each of them read by substituting tt back into the original equations:For Maya: Pm=87+2t=87+2(39)=87+78=165P_m = 87 + 2t = 87 + 2(39) = 87 + 78 = 165 pagesFor Ariel: Pa=9+4t=9+4(39)=9+156=165P_a = 9 + 4t = 9 + 4(39) = 9 + 156 = 165 pages

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