Question

Melissa, Chris, and Jim served a total of 76 orders Monday at the school cafeteria. Melissa served 8 fewer orders than Chris. Jim served 2 times as many ordersas Chris. How many orders did they each serve?x5?Number of orders Melissa served:Number of orders Chris served:Number of orders Jim served:000

Answer 1

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:

`x+y+z=76\text{ (eq. 1)}`

Given that Melissa served 8 fewer orders than Chris, then:

`x=y-8\text{ (eq. 2)}`

Given that Jim served 2 times as many orders as Chris, then:

`z=2y\text{ (eq. 3)}`

Substituting equations 2 and 3 into equation 1, and solving for y:

`\begin{gathered} (y-8)+y+2y=76 \\ (y+y+2y)-8=76 \\ 4y-8=76 \\ 4y-8+8=76+8 \\ 4y=84 \\ (4y)/(4)=(84)/(4) \\ y=21 \end{gathered}`

Substituting y = 21 into equations 2 and 3:

`\begin{gathered} x=21-8=13 \\ z=2\cdot21=42 \end{gathered}`

The final answer is:

• Number of orders Melissa served: ,13

,

• Number of orders Chris served: ,21

,

• Number of orders Jim served: ,42