Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. At the Oak Grove Ice Cream Parlor, one group of friends ordered 2 small servings of ice cream and 3 large servings of ice cream for $22. Another group of friends ordered 4 small servings of ice cream and 3 large servings of ice cream for $26. How much does the ice cream cost? The ice cream costs $_____ for a small serving and $_____ for a large serving.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  At the Oak Grove Ice Cream Parlor, one group of friends ordered 2 small servings of ice cream and 3 large servings of ice cream for $22. Another group of friends ordered 4 small servings of ice cream and 3 large servings of ice cream for $26. How much does the ice cream cost?  The ice cream costs $_____ for a small serving and $_____ for a large serving.

Bytelearn · Accepted Answer

Define Variables: Let's denote the cost of a small serving of ice cream as 's' and the cost of a large serving of ice cream as 'l'. The first group's order can be represented by the equation: 2s + 3l = 22First Group's Order: The second group's order can be represented by the equation: 4s + 3l = 26System of Equations: We now have a system of equations: 2s + 3l = 22 4s + 3l = 26 We can use either substitution or elimination to solve this system. Let's use elimination to solve for one of the variables.Elimination Method: To eliminate 'l', we can subtract the first equation from the second equation: (4s + 3l) - (2s + 3l) = 26 - 22 4s - 2s + 3l - 3l = 4 2s = 4 s = 2Substitute and Solve: Now that we have the value of 's', we can substitute it back into one of the original equations to find 'l'. Let's use the first equation: 2(2) + 3l = 22 4 + 3l = 22 3l = 22 - 4 3l = 18 l = 6

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