Question

An elevator can hold a maximum of 1500 pounds. An average child weighs 75 pounds and the average adult weighs 150 pounds. The elevator also can’t fit more than 14 people. How many children and adults can fit in the elevator and stay under the weight limit. Write the inequalities that represent the word problem, and then graph it on DESMOS. What is a solution that represents the amount of children and adults and their combined weight?

Answer 1

Let's take this problem step-by-step:

Let's first set up some variables:

• c: # of children
• a: # of adults

Let's examine the information given:

• Elevator can hold a maximum of 1500 pounds

          ⇒ average child is 75 pounds

          ⇒ average adult is 150 pounds

                 ⇒ therefore: $75c + 150a\leq 1500$

• Elevator can fit no more than 14 people

          ⇒ therefore: $c + a \leq 14$

Let's graph the equations:

 $75c+150a\leq 1500\\c+a\leq 14$

    ⇒ look at the image attached

The point at which the two graphs intersect:

  ⇒ is the solution that represents the amount of children and adults and

      their combine weight

With the horizontal axis being the # of children and vertical axis being the # of adults:

 ⇒ the solution is 8 children and 6 adults

Answer: 8 children and 6 adults

Hope that helped!