Question

Laura, Sam, and Miguel served a total of 121 orders Monday at the school cafeteria, Miguel served 7 fewer orders than Laura. Sam served 4 times as manyorders as Miguel. How many orders did they each serve?Number of orders Laura served:Number of orders Sam served:Number of orders Miguel served:

Answer 1

Let L, S, and M, denote the number of orders served by Laura, Sam, and Mighuel, respectively, on Monday at the school cafeteria.

Given that the total 121 orders were served,

`L+S+M=121\ldots(1)`

Given that Miguel served 7 fewer orders than Laura,

`\begin{gathered} M=L-7 \\ L=M+7 \end{gathered}`

Given that Sam served 4 times as many orders as Miguel,

`\begin{gathered} S=4\cdot M \\ S=4M \end{gathered}`

Substitute the values of 'L' and 'S' in equation (1),

`(M+7)+(4M)+M=121`

Simplify the above expression,

`\begin{gathered} M+7+4M+M=121 \\ 6M+7=121 \\ 6M=121-7 \\ M=(121-7)/(6) \\ M=19 \end{gathered}`

The corresponding values of L and S will be,

`\begin{gathered} L=19+7=26 \\ S=4\cdot19=76 \end{gathered}`

Thus, Laura served 26 orders, Sam served 76 orders, while MIguel served 19 orders on Monday at the school cafeteria.