Pre-Calculus Help: Get Answers to Problems for Homeschoolers

[Patsmatrix]

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!

 

[singleton]

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)

 

[Patsmatrix]

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.

 

[NateTG]

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?

 

[Patsmatrix]

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.

 

[singleton]

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 :)

 

[singleton]

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%.

 

[NateTG]

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?

 

[Patsmatrix]

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.