Question

Enterprise rents small vans to the Salvation Army to help deliver hot meals to senior citizens. Each van can only carry 1,200 pounds (lbs) of people and gear for safety reasons. The vans transport a number of volunteers to a central location to start deliveries from. Each person will deliver a single meal per trip. Assume the average weight of a person is 150 pounds. Each van will require 200 pounds of gear to keep the meal hot during transport, plus 10 pounds for each meal that will be delivered.

a) Create an inequality describing the restrictions on the number of people possible in a van. Graph the solution set.





b) A group of five volunteers wish to rent a van. What is the maximum average weight that the five volunteers can weigh and still be able to rent a van? Justify your answers.

Answer 1

Answer:

inverseoperations

Step-by-step explanation:

Answer 2

An inequality is used to represent unequal expressions or numbers. The inequality describing the restrictions on the number of people possible in a van is $160n + 200 \le 1200$.

Given that:

$Total = 1200$ --- total pounds the van can contain

$Weight = 150$ --- average weight of each person

$Gear = 200$ -- weight of the gear in a van

$Meal =10$ -- weight of each meal

Assume there are n people.

The total weight (T) of the n people is:

$T = Weight \times n$

Substitute $Weight = 150$

$T = 150 \times n$

$T = 150n$

The total weight (M) of the meals is:

$M= Meal \times n$

Substitute $Meal =10$

$M= 10\times n$

$M= 10n$

Because the van cannot contain more than 1200 pounds, we use less than or equal to as the inequality.

So, the inequality is:

$T + M + Gear \le 1200$

$150n + 10n + 200 \le 1200$

$160n + 200 \le 1200$

Hence, the inequality is: $160n + 200 \le 1200$

The solution to the inequality is as follows:

$160n + 200 \le 1200$

Collect like terms

$160n \le 1200-200$

$160n \le 1000$

Divide both sides by 160

$n \le 6.25$

Remove the decimal part (do not approximate)

$n \le 6$

Hence, the vehicle cannot contain more than 6 people.

See attachment for graph

Read more about inequalities at:

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