Variables
• x: Number of orders Melissa served
,• y: Number of orders Chris served
,• z: Number of orders Jim served
Given that they served a total of 76 orders, then:
[tex]x+y+z=76\text{ (eq. 1)}[/tex]Given that Melissa served 8 fewer orders than Chris, then:
[tex]x=y-8\text{ (eq. 2)}[/tex]Given that Jim served 2 times as many orders as Chris, then:
[tex]z=2y\text{ (eq. 3)}[/tex]Substituting equations 2 and 3 into equation 1, and solving for y:
[tex]\begin{gathered} (y-8)+y+2y=76 \\ (y+y+2y)-8=76 \\ 4y-8=76 \\ 4y-8+8=76+8 \\ 4y=84 \\ \frac{4y}{4}=\frac{84}{4} \\ y=21 \end{gathered}[/tex]Substituting y = 21 into equations 2 and 3:
[tex]\begin{gathered} x=21-8=13 \\ z=2\cdot21=42 \end{gathered}[/tex]The final answer is:
• Number of orders Melissa served: ,13
,• Number of orders Chris served: ,21
,• Number of orders Jim served: ,42