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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.At the Middletown Ice Cream Parlor, one group of friends ordered small servings of ice cream and large servings of ice cream for . Another group of friends ordered small servings of ice cream and large servings of ice cream for . How much does the ice cream cost?The ice cream costs for a small serving and for a large serving.
Full solution
Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.At the Middletown Ice Cream Parlor, one group of friends ordered small servings of ice cream and large servings of ice cream for . Another group of friends ordered small servings of ice cream and large servings of ice cream for . How much does the ice cream cost?The ice cream costs for a small serving and for a large serving.
- Write Equations: Write the system of equations based on the orders.First group's order: small servings () and large servings () for .Second group's order: small servings () and large servings () for .The system of equations is:
- Eliminate Variable: Decide which variable to eliminate.We can eliminate variable by multiplying the second equation by and adding it to the first equation.
- Multiply Second Equation: Multiply the second equation by -2.5＂).\(\newline\$-2.5(2s + 5l) = -2.5(24)\)\(\newline\)\(-5s - 12.5l = -60\)
- Add Equations: Add the new equation to the first equation to eliminate \(s\).\((5s + 5l) + (-5s - 12.5l) = 30 + (-60)\)\(5s - 5s + 5l - 12.5l = 30 - 60\)\(0s - 7.5l = -30\)
- Solve for \(l\): Solve for \(l\).\(-7.5l = -30\)\(l = \frac{-30}{-7.5}\)\(l = 4\)
- Substitute and Solve for \(s\): Substitute the value of \(l\) into one of the original equations to solve for \(s\). Using the second equation: \(2s + 5l = 24\) \(2s + 5(4) = 24\) \(2s + 20 = 24\) \(2s = 24 - 20\) \(2s = 4\) \(s = \frac{4}{2}\) \(s = 2\)
- Final Answer: Write the final answer.\(\newline\)The ice cream costs \(\$2\) for a small serving and \(\$4\) for a large serving.
