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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineAn event planner routinely orders ice sculptures for the corporate events she plans. For an executive dinner in Richmond, she ordered 22 small ice sculptures and 33 large ice sculptures, which cost $546\$546. Then, for a release party in Bluepoint, she ordered 55 small ice sculptures and 33 large ice sculptures, which cost a total of $717\$717. How much does each ice sculpture cost?\newlineEach small ice sculpture costs $____\$\_\_\_\_, and each large one costs $_____\$\_\_\_\_\_.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineAn event planner routinely orders ice sculptures for the corporate events she plans. For an executive dinner in Richmond, she ordered 22 small ice sculptures and 33 large ice sculptures, which cost $546\$546. Then, for a release party in Bluepoint, she ordered 55 small ice sculptures and 33 large ice sculptures, which cost a total of $717\$717. How much does each ice sculpture cost?\newlineEach small ice sculpture costs $____\$\_\_\_\_, and each large one costs $_____\$\_\_\_\_\_.
  1. Define Equations: Let's denote the cost of a small ice sculpture as SS and the cost of a large ice sculpture as LL. We can write two equations based on the information given:\newlineFor the executive dinner in Richmond: 2S+3L=$5462S + 3L = \$546\newlineFor the release party in Bluepoint: 5S+3L=$7175S + 3L = \$717
  2. Eliminate Variable: To solve this system using elimination, we want to eliminate one of the variables. We can do this by subtracting the first equation from the second equation to eliminate LL: \newline(5S+3L)−(2S+3L)=($717)−($546)(5S + 3L) - (2S + 3L) = (\$717) - (\$546)
  3. Solve for S: Perform the subtraction to eliminate L and solve for S:\newline5S−2S+3L−3L=($)717−($)5465S - 2S + 3L - 3L = (\$)717 - (\$)546\newline3S=($)1713S = (\$)171
  4. Substitute and Solve: Now, divide both sides by 33 to find the value of S:\newline3S÷3=($171)÷33S \div 3 = (\$171) \div 3\newlineS=($57)S = (\$57)
  5. Calculate 2S2S: With the value of SS found, we can substitute it back into one of the original equations to find LL. Let's use the first equation:\newline2S+3L=$5462S + 3L = \$546\newline2($57)+3L=$5462(\$57) + 3L = \$546
  6. Solve for L: Calculate the value of 22 times S:\newline2×$57=$1142 \times \$57 = \$114\newlineSo, the equation becomes:\newline$114+3L=$546\$114 + 3L = \$546
  7. Find Value of L: Subtract $114\$114 from both sides to solve for L:\newline3L=$546−$1143L = \$546 - \$114\newline3L=$4323L = \$432
  8. Find Value of L: Subtract $114\$114 from both sides to solve for L:\newline3L=$546−$1143L = \$546 - \$114\newline3L=$4323L = \$432Now, divide both sides by 33 to find the value of L:\newline3L÷3=$432÷33L \div 3 = \$432 \div 3\newlineL=$144L = \$144

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