Question

Renna pushed the button for the elevator to go up, but it would not move. The weight limit for the elevator is 450 kilograms, but the current group of passengers weighs a total of 750 kilograms. Renna wants to determine how many 70-kilogram passengers need to get off the elevator. Let p represent the number of excess passengers. Write an inequality to determine the number of passengers who need to get off the elevator to meet the weight requirement.

Answer 1

First we should figure out how much over the weight limit the passengers are. We can find this by 750-450 which is 300. The amount of weight that needs to get off the elevator is 300 kilograms. Then, we know that each passenger weighs 70 kilograms. We can represent this as 70p.The inequality is 70p \geq 300. Then we can solve by dividing both sides of the inequality by 70. We get p \geq 4.28... Since people only come in whole numbers, and it has to be greater than 4.28, the number of excess passengers is 5.

Hope this helped!

Answer 2

The inequality that the number of passengers who need to get off the elevator to meet the weight requirement is $\boxed{750-70p\leq450}$

Further explanation:

An inequality means that two values are not equal or it can be said that one value is greater or less than the other value.

For example: $a\neq b$

We use other symbols to write the relation between $a$ and $b$ as,

$a$ means that $a$ is less than $b$.

$a>b$ means that $a$ is greater than $b$.

$a\leq b$ means that $a$ is less than or equal to $b$.

$a\geq b$ means that $a$ is greater than or equal to $b$.

It is given that the weight limit for the elevator is $450\text{ kg}$, but the current group of passengers weighs a total of $750\text{ kg}$.

Let $p$ represent the number of excess passengers and Renna wants to determine $70\text{ kg}$ passengers that need to get off the elevator.

Therefore, the total number of excess passengers that weights $70\text{ kg}$ is $70p$.

So, the total weight after excluding the $p$ number of passengers is $750-70p$.

Since, the weight limit of the elevator is $450\text{ kg}$, this implies that the total weight of the passengers can be equal to $450\text{ kg}$ or it can be less than $450\text{ kg}$.

The inequality that the number of passengers who need to get off the elevator to meet the weight requirement is as follows:

$\boxed{750-70p\leq 450}$

The symbol $\leq$ represents that the passengers that are getting off can be equal to the weight limit of the lift.

Therefore, the inequality that the number of passengers who need to get off the elevator to meet the weight requirement is $\boxed{750-70p\leq 450}$.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Inequalities  

Keywords: Inequality, compound inequality, strict inequalities, function, sets, ordered sets, real numbers, integers, whole numbers, rational numbers, power inequality, less than, more than.