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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineEmily owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 44 small tiers and 44 large tiers, which will serve a total of 268268 guests. The second one includes 22 small tiers and 44 large tiers, which is enough servings for 228228 guests. How many guests does each size of tier serve?\newlineA small tier will serve _\_ guests and a large tier will serve _\_ guests.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineEmily owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 44 small tiers and 44 large tiers, which will serve a total of 268268 guests. The second one includes 22 small tiers and 44 large tiers, which is enough servings for 228228 guests. How many guests does each size of tier serve?\newlineA small tier will serve _\_ guests and a large tier will serve _\_ guests.
  1. Equation for first cake: Let's denote the number of guests served by a small tier as ss and by a large tier as ll. The first cake, serving 268268 guests, consists of 44 small tiers and 44 large tiers, leading to the equation 4s+4l=2684s + 4l = 268.
  2. Equation for second cake: The second cake serves 228228 guests with 22 small tiers and 44 large tiers, giving us the equation 2s+4l=2282s + 4l = 228.
  3. Eliminating variable ss: To eliminate one variable, we'll focus on eliminating ss. Multiply the second equation by 22 to align the coefficients of ss with the first equation: 4s+8l=4564s + 8l = 456.
  4. Subtracting equations: Subtract the first equation from the modified second equation: 4s+8l)−(4s+4l)=456−268 simplifyingto$4l=1884s + 8l) - (4s + 4l) = 456 - 268\, simplifying to \$4l = 188.
  5. Solving for l: Solve for ll: l=1884l = \frac{188}{4}, which equals 4747.
  6. Substitute ll into first equation: Substitute l=47l = 47 back into the first equation: 4s+4×47=2684s + 4\times47 = 268. This simplifies to 4s+188=2684s + 188 = 268.
  7. Solving for s: Solve for s: 4s=268−1884s = 268 - 188, which simplifies to 4s=804s = 80. Then, s=804s = \frac{80}{4}, which equals 2020.

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