Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Bryan is a server at an all-you-can eat sushi restaurant. At one table, the customers ordered 2 child buffets and 3 adult buffets, which cost a total of $121. At another table, the customers ordered 3 child buffets and 3 adult buffets, paying a total of $138. How much does the buffet cost for each child and adult? The cost for a child is $_____, and the cost for an adult is $_____.

Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.  Bryan is a server at an all-you-can eat sushi restaurant. At one table, the customers ordered 2 child buffets and  3 adult buffets, which cost a total of $121. At another table, the customers ordered 3 child buffets and  3 adult buffets, paying a total of $138. How much does the buffet cost for each child and adult?  The cost for a child is $_____, and the cost for an adult is $_____.

Bytelearn · Accepted Answer

Define Variables: 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'. At one table, the equation for the total cost is: 2c + 3a = 121Equation at Table 1: At another table, the equation for the total cost is: 3c + 3a = 138Equation at Table 2: We now have a system of equations: 2c + 3a = 121 3c + 3a = 138 We can solve this system using the method of elimination or substitution. Let's use elimination to solve for 'c' and 'a'.System of Equations: Subtract the first equation from the second to eliminate 'a': (3c + 3a) - (2c + 3a) = 138 - 121 3c - 2c + 3a - 3a = 17 c = 17Elimination Method: Now that we have the value of 'c', we can substitute it back into one of the original equations to find 'a'. Let's use the first equation: 2(17) + 3a = 121 34 + 3a = 121 3a = 121 - 34 3a = 87 a = 87 / 3 a = 29Substitute for c: We have found the values for 'c' and 'a': c = 17 a = 29 The cost for a child buffet is $17, and the cost for an adult buffet is $29.

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