equations and Inequalites

User Generated

zbeny411

Mathematics

Description

Each boat can carry 1200 lbs of people and gear for safety reasons. Assume the average weight of a person is 150 lbs. Each group will require 200 lbs of gear for the boat plus 10 lbs of gear for each person. Part1: create a inequality describing the restrictions on the number of ,p, possible in a rented boat. Part2:find the solution to your inequality. In other words how many people can attend the trip. Write this as an inequality, use p, to represent the number of people.

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Explanation & Answer

Number of people in a boat = p

Maximum weight carried by a boat = 1200 lbs

Average weight of a person = 150 lbs

so, total weight of the people on boat = 150*p

Per person weight of gear = 10 lbs

so, total weight of gear (for people) on boat = 10*p

Weight of gear required for boat = 200 lbs

Now, total weight on the boat should be less than or equal to the maximum allowed weight i.e. 1200 lbs

therefore,

150*p + 10*p + 200 <= 1200

160*p <= 1000

1. The required inequality is 160*p <= 1000

2. solve for p

160*p <= 1000

p <= 1000/160

p <= 25/4

As p is the number of people, it has to be a whole number

therefore, p<= 6

or, Maximum of 6 people can ride on the boat 


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