Question

An elevator can carry 800 pounds of weight.

a. A student weighing 95 pounds gets on the elevator. Write and solve an inequality to represent the remaining weight that can be added.
b. A football player weighing 280 pounds gets on the elevator with the student. Write and solve an inequality representing the remaining weight that can be added.
c. Two more football players weighing a total of 470 pounds come to the elevator. Can they get on safely? Explain.
a. 625≤x≤800, Yes
b. 445≤x≤800, No
c. 350≤x≤800, No

Answer 1

For the following:

• a) The correct inequality for the remaining weight after the student gets on is
  `\( x \leq 705 \)`, not
  `\( 625 \leq x \leq 800 \)`.
• b) After the football player gets on with the student, the correct inequality is
  `\( x \leq 425 \)`, not
  `\( 445 \leq x \leq 800 \)`.
• c) The two additional football players cannot get on safely, as their combined weight with the others exceeds 800 pounds.

How to solve inequalities?

Calculate the remaining weight capacity of the elevator after each person gets on, and then determine if additional weight can be safely added without exceeding the elevator's maximum capacity of 800 pounds.

a) A student weighing 95 pounds gets on the elevator.

The remaining weight capacity can be represented by an inequality. Let x represent the additional weight that can be added. The inequality is:

`\[ 95 + x \leq 800 \]`

To solve for x:

`\[ x \leq 800 - 95 \]`

`\[ x \leq 705 \]`

So, the inequality representing the remaining weight that can be added is
`\( x \leq 705 \)`.

b) A football player weighing 280 pounds gets on the elevator with the student.

The total weight on the elevator now is 95 + 280 pounds. The inequality for the remaining weight capacity is:

`\[ 95 + 280 + x \leq 800 \]`

Solving for x:

`\[ x \leq 800 - 95 - 280 \]`

`\[ x \leq 425 \]`

Therefore, the inequality representing the remaining weight that can be added is
`\( x \leq 425 \)`.

c) Two more football players weighing a total of 470 pounds come to the elevator.

The total weight with the two additional football players is
`\( 95 + 280 + 470 \)` pounds. To check if they can get on safely:

`\[ 95 + 280 + 470 \leq 800 \]`

`\[ 845 \leq 800 \]`

This is not true; 845 pounds exceeds the elevator's maximum capacity. Therefore, they cannot get on safely.