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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ At the Castroville Ice Cream Parlor, one group of friends ordered $1$ small serving of ice cream and $3$ large servings of ice cream for $20$ . Another group of friends ordered $1$ small serving of ice cream and $4$ large servings of ice cream for $26$ . How much does the ice cream cost? $\newline$ The ice cream costs `\$`_ for a small serving and `\$`_ for a large serving.

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Solve a system of equations using elimination: word problems

Full solution

Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

At the Castroville Ice Cream Parlor, one group of friends ordered

1

small serving of ice cream and

3

large servings of ice cream for

20

. Another group of friends ordered

1

small serving of ice cream and

4

large servings of ice cream for

26

. How much does the ice cream cost?

\newline

The ice cream costs `\$`_____ for a small serving and `\$`_____ for a large serving.

First Group's Order: First group's order: $1$ small + $3$ large = $\$20$ . $\newline$ Let $x$ be the cost of a small serving and $y$ be the cost of a large serving. $\newline$ Equation: $x + 3y = 20$ .
Second Group's Order: Second group's order: $1$ small + $4$ large = $\$26$ . $\newline$ Equation: $x + 4y = 26$ .
Eliminate Variable: To eliminate a variable, subtract the first equation from the second. $(x + 4y) - (x + 3y) = 26 - 20$ .
Simplify Subtraction: Simplify the subtraction: $x + 4y - x - 3y = 26 - 20$ . This simplifies to $y = 6$ .
Substitute and Calculate: Substitute $y = 6$ into the first equation: $x + 3(6) = 20$ . Calculate $x$ : $x + 18 = 20$ .
Solve for x: Solve for x: $x = 20 - 18$ . $\newline$ $x = 2$ .

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