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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA caterer is making cookie trays for upcoming holiday parties. This morning, she made 44 small trays and 11 large tray, which contain a total of 103103 cookies. In the afternoon, she made 44 small trays and 22 large trays, which contain a total of 158158 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 elimination, and fill in the blanks.\newlineA caterer is making cookie trays for upcoming holiday parties. This morning, she made 44 small trays and 11 large tray, which contain a total of 103103 cookies. In the afternoon, she made 44 small trays and 22 large trays, which contain a total of 158158 cookies. How many cookies do the different sized trays contain?\newlineThe small tray contains _\_ cookies and the large one contains _\_ cookies.
  1. Equations Setup: Let's denote the number of cookies in a small tray as SS and the number of cookies in a large tray as LL. We can then write two equations based on the given information.\newlineEquation 11 (from the morning batch): 4S+1L=1034S + 1L = 103\newlineEquation 22 (from the afternoon batch): 4S+2L=1584S + 2L = 158
  2. Elimination Method: To use elimination, we want to eliminate one of the variables. We can do this by multiplying the first equation by 22, so that the coefficients of LL in both equations match.\newlineMultiplying the first equation by 22 gives us: 8S+2L=2068S + 2L = 206
  3. Subtracting Equations: Now we have the system of equations:\newline8S+2L=2068S + 2L = 206\newline4S+2L=1584S + 2L = 158\newlineWe can subtract the second equation from the first to eliminate LL.\newline(8S+2L)−(4S+2L)=206−158(8S + 2L) - (4S + 2L) = 206 - 158
  4. Solving for S: Performing the subtraction, we get:\newline8S−4S+2L−2L=206−1588S - 4S + 2L - 2L = 206 - 158\newline4S=484S = 48
  5. Substitute and Solve for L: Now we can solve for SS by dividing both sides of the equation by 44.4S4=484\frac{4S}{4} = \frac{48}{4}S=12S = 12
  6. Substitute and Solve for L: Now we can solve for SS by dividing both sides of the equation by 44.
    4S4=484\frac{4S}{4} = \frac{48}{4}
    S=12S = 12Now that we have the value for SS, we can substitute it back into one of the original equations to solve for LL. We'll use the first equation:
    4S+1L=1034S + 1L = 103
    4(12)+L=1034(12) + L = 103
  7. Substitute and Solve for L: Now we can solve for SS by dividing both sides of the equation by 44.
    4S4=484\frac{4S}{4} = \frac{48}{4}
    S=12S = 12Now that we have the value for SS, we can substitute it back into one of the original equations to solve for LL. We'll use the first equation:
    4S+1L=1034S + 1L = 103
    4(12)+L=1034(12) + L = 103Substitute S=12S = 12 into the equation and solve for LL:
    4400
    4411
    4422

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