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Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineA caterer is making cookie trays for upcoming holiday parties. This morning, she made 11 large tray, which contain a total of 6060 cookies. In the afternoon, she made 55 small trays and 33 large trays, which contain a total of 255255 cookies. How many cookies do the different sized trays contain?\newlineThe small tray contains ____\_\_\_\_ cookies and the large one contains ____\_\_\_\_ cookies.

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Q. Write a system of equations to describe the situation below, solve using an augmented matrix, and fill in the blanks.\newlineA caterer is making cookie trays for upcoming holiday parties. This morning, she made 11 large tray, which contain a total of 6060 cookies. In the afternoon, she made 55 small trays and 33 large trays, which contain a total of 255255 cookies. How many cookies do the different sized trays contain?\newlineThe small tray contains ____\_\_\_\_ cookies and the large one contains ____\_\_\_\_ cookies.
  1. Define Variables: Let xx be the number of cookies in a small tray and yy be the number of cookies in a large tray. The first equation is based on the morning's work: 1y=601y = 60.
  2. Form Equations: The second equation is based on the afternoon's work: 5x+3y=2555x + 3y = 255.
  3. Solve Using Matrix: We can write the system of equations as an augmented matrix and solve using row operations: [1amp;0amp;∣amp;60 5amp;3amp;∣amp;255]\begin{bmatrix} 1 & 0 & | & 60 \ 5 & 3 & | & 255 \end{bmatrix}
  4. Determine yy Value: Since the first row already shows that 11 large tray contains 6060 cookies, we know that y=60y = 60.
  5. Substitute yy in Equation: Now we need to use the second row to find the value of xx. We can replace yy with 6060 in the second equation: 5x+3(60)=2555x + 3(60) = 255.
  6. Simplify Equation: Simplify the equation: 5x+180=2555x + 180 = 255.
  7. Subtract 180180: Subtract 180180 from both sides: 5x=255−1805x = 255 - 180.
  8. Calculate x Value: Calculate the value of x: 5x=755x = 75.
  9. Divide by 55: Divide both sides by 55 to find xx: x=755x = \frac{75}{5}.
  10. Final x Value: Calculate the final value of x: x=15x = 15. Oops, made a mistake here, should have been x=755=15x = \frac{75}{5} = 15.

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