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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. Bert can read 11 page per minute, and he had already read 7979 pages. Preston, who has a reading speed of 33 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, Bert and Preston 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. Bert can read 11 page per minute, and he had already read 7979 pages. Preston, who has a reading speed of 33 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, Bert and Preston had each read _\_ pages.
  1. Define Variables: Let's define the variables:\newlineLet xx represent the number of minutes after they start reading together.\newlineLet BB represent the total number of pages Bert has read.\newlineLet PP represent the total number of pages Preston has read.
  2. Write Equations: We can write two equations to represent the situation:\newlineFor Bert: B=79+1×xB = 79 + 1 \times x (since Bert reads 11 page per minute and had already read 7979 pages)\newlineFor Preston: P=9+3×xP = 9 + 3 \times x (since Preston reads 33 pages per minute and had already read 99 pages)
  3. Set Equations Equal: Since they eventually read the same number of pages, we can set the two equations equal to each other:\newline79+x=9+3x79 + x = 9 + 3x
  4. Solve for x: Now, we solve for xx using substitution:\newline79+x=9+3x79 + x = 9 + 3x\newlineSubtract xx from both sides:\newline79=9+2x79 = 9 + 2x
  5. Isolate x Term: Subtract 99 from both sides to isolate the term with xx: \newline79−9=2x79 - 9 = 2x\newline70=2x70 = 2x
  6. Find x Value: Divide both sides by 22 to solve for x:\newline702=x\frac{70}{2} = x\newline35=x35 = x
  7. Find Pages Read: Now that we have the value for xx, we can find out how many pages each of them read:\newlineFor Bert: B=79+1×35=79+35=114B = 79 + 1 \times 35 = 79 + 35 = 114 pages\newlineFor Preston: P=9+3×35=9+105=114P = 9 + 3 \times 35 = 9 + 105 = 114 pages

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