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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 Lakewood, she ordered 44 small ice sculptures and 55 large ice sculptures, which cost $871\$871. Then, for a release party in Danville, she ordered 55 small ice sculptures and 22 large ice sculptures, which cost a total of $549\$549. 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 Lakewood, she ordered 44 small ice sculptures and 55 large ice sculptures, which cost $871\$871. Then, for a release party in Danville, she ordered 55 small ice sculptures and 22 large ice sculptures, which cost a total of $549\$549. How much does each ice sculpture cost?\newlineEach small ice sculpture costs $\$____, and each large one costs $\$_____.
  1. Equations Setup: Let's denote the cost of a small ice sculpture as SS and the cost of a large ice sculpture as LL. We can then write two equations based on the information given:\newlineFor the executive dinner in Lakewood: 4S+5L=$8714S + 5L = \$871\newlineFor the release party in Danville: 5S+2L=$5495S + 2L = \$549
  2. Elimination Method: To solve this system using elimination, we want to eliminate one of the variables. We can do this by multiplying the second equation by 22, so that the coefficient of LL in both equations is the same:\newline2×(5S+2L)=2×($549)2\times(5S + 2L) = 2\times(\$549)\newlineThis gives us: 10S+4L=($1098)10S + 4L = (\$1098)
  3. New System of Equations: Now we have the system of equations:\newline4S+5L=$(871)4S + 5L = \$(871)\newline10S+4L=$(1098)10S + 4L = \$(1098)\newlineWe can eliminate LL by multiplying the first equation by 44 and the second equation by 55 and then subtracting the second equation from the first:\newline4∗(4S+5L)=4∗$(871)4*(4S + 5L) = 4*\$(871)\newline5∗(10S+4L)=5∗$(1098)5*(10S + 4L) = 5*\$(1098)\newlineThis gives us: 16S+20L=$(3484)16S + 20L = \$(3484)\newlineand: 50S+20L=$(5490)50S + 20L = \$(5490)
  4. Solving for S: Subtract the second equation from the first:\newline(16S+20L)−(50S+20L)=($)3484−($)5490(16S + 20L) - (50S + 20L) = (\$)3484 - (\$)5490\newline−34S=−($)2006-34S = -(\$)2006\newlineNow, divide both sides by −34-34 to solve for S:\newlineS=($)2006/34S = (\$)2006 / 34\newlineS=($)59S = (\$)59
  5. Substitute S to Find L: Now that we have the value for S, we can substitute it back into one of the original equations to solve for L. Let's use the first equation:\newline4S+5L=$8714S + 5L = \$871\newline4∗$59+5L=$8714*\$59 + 5L = \$871\newline$236+5L=$871\$236 + 5L = \$871\newline5L=$871−$2365L = \$871 - \$236\newline5L=$6355L = \$635\newlineNow, divide both sides by 55 to solve for L:\newlineL=$635/5L = \$635 / 5\newlineL=$127L = \$127

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