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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineAn employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed 44 small chandeliers and 22 large chandeliers, which weighed a total of 6666 kilograms. In the second box, he packed 44 small chandeliers and 44 large chandeliers, which had a weight of 112112 kilograms. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?\newlineEach small chandelier weighs _\_ kilograms and each large one weighs _\_ kilograms.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineAn employee at a company that assembles chandeliers is packing boxes for shipping. In the first box, he packed 44 small chandeliers and 22 large chandeliers, which weighed a total of 6666 kilograms. In the second box, he packed 44 small chandeliers and 44 large chandeliers, which had a weight of 112112 kilograms. Assuming the weight of the box isn't included in the shipping weight, how much does each size of chandelier weigh?\newlineEach small chandelier weighs _\_ kilograms and each large one weighs _\_ kilograms.
  1. Denote weights: Let's denote the weight of each small chandelier as ss and the weight of each large chandelier as ll. The first box with 44 small chandeliers and 22 large chandeliers weighs a total of 6666 kilograms, which gives us the equation 4s+2l=664s + 2l = 66.
  2. First box equation: The second box with 44 small chandeliers and 44 large chandeliers weighs 112112 kilograms, which gives us the equation 4s+4l=1124s + 4l = 112.
  3. Second box equation: We now have a system of two equations. To use elimination, we can subtract the first equation from the second equation to eliminate ss. Subtracting 4s+2l=664s + 2l = 66 from 4s+4l=1124s + 4l = 112 gives us 2l=462l = 46.
  4. Elimination method: Dividing both sides of 2l=462l = 46 by 22 gives us l=23l = 23. This means each large chandelier weighs 2323 kilograms.
  5. Large chandelier weight: Now that we know the weight of each large chandelier, we can substitute l=23l = 23 into the first equation 4s+2l=664s + 2l = 66 to find the weight of each small chandelier. Substituting ll gives us 4s+2(23)=664s + 2(23) = 66.
  6. Substitute in first equation: Simplifying the equation 4s+46=664s + 46 = 66 by subtracting 4646 from both sides gives us 4s=204s = 20.
  7. Find small chandelier weight: Dividing both sides of 4s=204s = 20 by 44 gives us s=5s = 5. This means each small chandelier weighs 55 kilograms.

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