Question

renna pushes the elevator button, but the elevator does not move. the mass limit for the elevator is 450 kilograms (kg), but renna and her load of identical packages mass a total of 620 kg. each package has a mass of 37.4 kg.
write an inequality to determine the number of packages, p, renna could remove from the elevator to meet the mass requirement.
what is the minimum whole number of packages renna needs to remove from the elevator to meet the mass requirement?

Explanation:

Step1: Set up the inequality

The total mass is \(620\) kg. Each package has a mass of \(37.4\) kg. If we remove \(p\) packages, the remaining mass is \(620 - 37.4p\). This remaining mass must be less than or equal to the mass - limit of \(450\) kg. So the inequality is \(620 - 37.4p\leqslant450\).

Step2: Solve the inequality for \(p\)

First, subtract \(620\) from both sides:
\(-37.4p\leqslant450 - 620\)
\(-37.4p\leqslant - 170\)
Then divide both sides by \(-37.4\). When dividing by a negative number, the inequality sign flips:
\(p\geqslant\frac{-170}{-37.4}\approx4.54545\)

Since \(p\) represents the number of packages and it must be a whole number, we round up to the next whole number. So \(p = 5\).

Answer:

1. \(620 - 37.4p\leqslant450\)
2. \(5\)