Pre-Calculus Help: Get Answers to Problems for Homeschoolers

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    Pre-calculus
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Discussion Overview

The discussion revolves around solving pre-calculus problems, specifically focusing on a rectangular plot's dimensions, collaborative work rates, and a salt solution concentration problem. Participants share their approaches and seek assistance with the calculations involved.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a method to find the dimensions of a rectangular plot based on its perimeter and the relationship between length and width.
  • Another participant confirms the perimeter formula and provides a step-by-step solution for the first problem, arriving at a width of 68 m and a length of 93 m.
  • Participants express varying levels of difficulty with the second and third problems, with one noting that the second problem is easier than the third.
  • For the salt solution problem, participants discuss the initial and final concentrations of salt, with one participant calculating the amount of salt in the initial solution.
  • There is a suggestion to focus on the constant amount of salt during evaporation, which leads to a discussion about finding the correct quantities to achieve the desired concentration.
  • One participant claims to have found the answer to the salt solution problem, stating that 96 gallons need to be evaporated, but still struggles with the second problem.

Areas of Agreement / Disagreement

Participants generally agree on the methods for solving the problems, but there is no consensus on the second problem, as one participant continues to express difficulty with it.

Contextual Notes

Some participants express uncertainty about their calculations and the processes involved, particularly in the salt solution problem. The discussion reflects varying levels of understanding and confidence in pre-calculus concepts.

Patsmatrix
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Help!

I'm having trouble with a few problems.. I'm a Homeschooler, and my teacher is away for a while, so I need a bit of help figuring these problems out.

1. A flower seed company has a rectangular test plot with a perimeter of 322 m. The length is 25 m more than the width. Find the dimensions of the plot.

2. Trent can deliver his newspapers in 30 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?

3. How much water must be evaporated from 240 gallons of a 3% salt solution to produce a 5% salt solution?

Note: I'm still just beginning PreCalculus, so I'm somewhat of a newbie to it.. So.. Help!
 
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1. Perimeter of a rectangular area is what? 2L + 2W, agree?
Let x represent the width.
Therefore x + 25 is the length
2(x + 25) + 2x = 322
2x + 50 + 2x = 322
4x + 50 = 322
4x = 322 - 50
4x = 272
x = 68 (width)
x + 25 = 93 (length)
 
singleton said:
1. Perimeter of a rectangular area is what? 2L + 2W, agree?
Let x represent the width.
Therefore x + 25 is the length
2(x + 25) + 2x = 322
2x + 50 + 2x = 322
4x + 50 = 322
4x = 322 - 50
4x = 272
x = 68 (width)
x + 25 = 93 (length)

Ahh.. Thank you! Number 2 is a little easier for me, but number 3 just makes my head keep spinning.
 
Patsmatrix said:
Ahh.. Thank you! Number 2 is a little easier for me, but number 3 just makes my head keep spinning.

Well, you can slog your way through it:
How much salt is there in the beginning?
How much salt is there at the end?
How much water is there at the end?
 
NateTG said:
Well, you can slog your way through it:
How much salt is there in the beginning?
How much salt is there at the end?
How much water is there at the end?

Er.. There's .03 (3%) salt in the beginning, and .05 (5%) in the end.. I'm just at a loss as to how to solve it from there.. It's as if my mind hits a brick wall.
 
3. How much water must be evaporated from 240 gallons of a 3% salt solution to produce a 5% salt solution?

In 240 gallons, 3% salt solution is what, 7.2 gallons worth of salt? (ignore for a moment that salt is not a liquid and gallons is used to measure liquid only--I think).

During evaporation only the water leaves, correct? The salt content remains same.

So, this is how I figured it. I may be quite wrong or this may be a very wrong process. Don't take my word since I'm a poor math student (I'm not kidding!).

Edit: ignore what I had I think it is wrong.
Realize the constant amount of salt and it should be easy to figure out :)
 
Last edited:
Patsmatrix said:
Er.. There's .03 (3%) salt in the beginning, and .05 (5%) in the end.. I'm just at a loss as to how to solve it from there.. It's as if my mind hits a brick wall.

Try not to think of how much salt there is at beginning and end. Realize that it is constant, right?

Once you find the salt, you just have to find the correct quantity of salt to water which will lend you the 5%.
 
Patsmatrix said:
Er.. There's .03 (3%) salt in the beginning, and .05 (5%) in the end.. I'm just at a loss as to how to solve it from there.. It's as if my mind hits a brick wall.

How about in absolute (instead of relative) amounts?
 
Thanks folks, I got the answer thanks to your help... 96 Gallons needed to be evaporated.

I'm still having problems with number 2 though.
 

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