Question

2. A certain elevator can hold a maximum weight of 2,800 pounds. This total is determined by estimating the average adult weight as 200 pounds and the average child weight as 80 pounds. Write an inequality that represents this situation, then graph it on the coordinate plane below. Determine a combination of children, c, and adults, a, that can safely ride the elevator.

Answer 1

Let's begin by listing out the given information

Elevator Max weight (e) = 2000 lb

Each adult's weight (a) = 200 lb

Each child's weight (c) = 80 lb

Our inequality is given by:

`200a+80c\le2000-----1`

We will proceed to find the combination of people that can safely ride the elevator

`\begin{gathered} 200a+80c\le2000 \\ \text{If there are 5 a}dults,\text{ we have:} \\ 200(5)+80c\le2000 \\ 1000+80c\le2000 \\ 80c\le2000-1000 \\ 80c\le1000 \\ c\le12.5(\text{that's 12 }children) \\ \text{If there are 8 a}dults,\text{ we have:} \\ 200(8)+80c\le2000 \\ 80c\le2000-1600 \\ 80c\le400 \\ c\le5(\text{5 }children) \end{gathered}`