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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ Ron is a server at an all-you-can eat sushi restaurant. At one table, the customers ordered $2$ child buffets and $2$ adult buffets, which cost a total of $\$82$ . At another table, the customers ordered $2$ child buffets and $3$ adult buffets, paying a total of $\$108$ . How much does the buffet cost for each child and adult? $\newline$ The cost for a child is $\$$ _, and the cost for an adult is $\$$ _.

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Solve a system of equations using any method: word problems

Full solution

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

\newline

Ron is a server at an all-you-can eat sushi restaurant. At one table, the customers ordered

2

child buffets and

2

adult buffets, which cost a total of

\$82

. At another table, the customers ordered

2

child buffets and

3

adult buffets, paying a total of

\$108

. How much does the buffet cost for each child and adult?

\newline

The cost for a child is

\$

_____, and the cost for an adult is

\$

_____.

Define Buffet Costs: Let's denote the cost of the child buffet as $c$ and the cost of the adult buffet as $a$ . We need to find the values of $c$ and $a$ .
First Table's Order: From the first table's order, we have the equation for the total cost of $2$ child buffets and $2$ adult buffets: $\newline$ $2c + 2a = \$(82)$
Second Table's Order: From the second table's order, we have the equation for the total cost of $2$ child buffets and $3$ adult buffets: $\newline$ $2c + 3a = \$(108)$
System of Equations: We now have a system of equations: $\newline$ $2c + 2a = \$(82)$ $\newline$ $2c + 3a = \$(108)$ $\newline$ We can solve this system using the method of elimination or substitution. Let's use elimination.
Elimination Method: Subtract the first equation from the second equation to eliminate ＂c＂: $\newline$ $(2c + 3a) - (2c + 2a) = (\$)108 - (\$)82$ $\newline$ $3a - 2a = (\$)26$ $\newline$ $a = (\$)26$
Find Cost of Adult Buffet: Now that we have the value of $a$ , we can substitute it back into one of the original equations to find $c$ . Let's use the first equation: $\newline$ $2c + 2(26) = (\$)82$ $\newline$ $2c + (\$)52 = (\$)82$ $\newline$ $2c = (\$)82 - (\$)52$ $\newline$ $2c = (\$)30$ $\newline$ $c = (\$)15$

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