SOLUTION: There are several elevators in the Sandy Beach Hotel. Each elevator can hold at most 12 people. Additionally, each elevator can only carry 1600 pounds of people and baggage for saf
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Question 1202250: There are several elevators in the Sandy Beach Hotel. Each elevator can hold at most 12 people. Additionally, each elevator can only carry 1600 pounds of people and baggage for safety reasons. Assume on average an adult weighs 175 pounds and a child weighs 70 pounds. Also assume each group will have 150 pounds of baggage plus 10 additional pounds of personal items per person.
Part A. Write a system of linear equations or inequalities that describes the weight limit for one group of adults and children on a Sandy Beach Hotel elevator and that represents the total number of passengers in a Sandy Beach Hotel elevator.
Part B. Several groups of people want to share the same elevator. Group 1 has 4 adults and 3 children. Group 2 has 1 adult and 11 children. Group 3 has 9 adults. Which of the groups, if any, can safely travel in a Sandy Beach elevator? Answer by math_tutor2020(3817) (Show Source):
x = number of adults
y = number of children
These variables are nonnegative integers 0,1,2,3,...
The elevator allows at most 12 people meaning that
Either x+y < 12, or x+y = 12
Now to the weight requirements.
Each adult weighs 175 pounds on average.
Add on 10 pounds of their personal belongings to see that each adult contributes a weight of 175+10 = 185 pounds.
x number of adults contribute 185x pounds
Each child weighs 70 pounds on average.
That bumps up to 80 pounds when considering their personal luggage.
Therefore, y number of children adds on 80y extra pounds.
The total weight so far is 185x+80y pounds.
Then add on the 150 pounds of luggage mentioned in the instructions.
This is the publicly shared luggage of the group (as opposed to the personal luggage).
Therefore, the total combined weight of each person and all luggage (personal or shared) is 185x+80y+150 pounds.
This total cannot exceed 1600 pounds.
This is the ceiling value.
Since we're dealing with an elevator, it is fitting to think of a hypothetical tower with 1600 floors as the highest we can go.
Feel free to come up with other metaphors.
This leads to the inequality
I'll let the student solve for y if the teacher requires it.
To recap everything we have these two inequalities
that represent the system of inequalities
A more narrowly defined system would be
which prevents x and y from being negative.
It makes no sense to have a negative number of people.
(