word problem help

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Travism1992

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A potting mixture contains 15.0% peat moss and 6.00% vermiculite. How much peat and how much vermiculite must be added to 75lbs of this mixture to produce a new mixture having 20.0% peat and 15.0% vermiculite? I can't figure out how to set it up, I'm sure I'm overthinking it, but would rather seek help to make sure I do this correctly. Thanks!
 
Travism1992 said:
A potting mixture contains 15.0% peat moss and 6.00% vermiculite. How much peat and how much vermiculite must be added to 75lbs of this mixture to produce a new mixture having 20.0% peat and 15.0% vermiculite? I can't figure out how to set it up, I'm sure I'm overthinking it, but would rather seek help to make sure I do this correctly. Thanks!
Click to expand...

Start with:

How much vermiculite is present in 75 lbs of old mixture?

How much peat-moss is present in 75 lbs of old mixture?

How much "other stuff" is present in 75 lbs of old mixture? this remains constant since we are adding Peat and Vermiculite.

Now what.....

Please share your work with us, indicating exactly where you are stuck so that we may know where to begin to help you.
 
Well i guess thats the issue, is I'm not sure how to set it up. i believe once i get it set up i will be able to finish from there.
 
Mixture probolem

Hello, Travism1992!

This was new one on me.
I had to baby-talk my way through it.

A potting mixture contains 15% peat moss and 6% vermiculite.
How much peat and how much vermiculite must be added to 75lbs of this mixture
to produce a new mixture having 20.0% peat moss and 15.0% vermiculite?
Click to expand...

Let \(\displaystyle p\) = amount of peat moss to be added.
Let \(\displaystyle v\) = amount of vermiculite to be added.
The final mixture contains \(\displaystyle 75 + p + v\) pounds.

The original mix is 75 lbs which is 15% peat moss.
. . It contains: \(\displaystyle (0.15)(75) \,=\,11.25\) lbs of peat moss.
The final mixture will contain: \(\displaystyle 11.25 + p\) lbs of peat moss. *

We know that the final mixture will be 20% peat moss.
. . It will contain: \(\displaystyle 0.20(75+p+v)\) lbs of peat moss. *

We just described the final amount of peat moss in two ways.
There is one of the equations: .\(\displaystyle 11.25 + p \:=\:0.20(75 + p+v)\) [1]


The original mix is 75 lbs which is 6% vermiculite.
. . It contains: \(\displaystyle (0.06)(75) \,=\,4.5\) lbs of vermiculite.
The final mixture will contain: \(\displaystyle 4.5 + v\) lbs of vermiculite. *

We know that the final mixture will be 15% vermiculite.
. . It will contain: \(\displaystyle 0.15(75+p+v)\) lbs of vermiculite. *

We just described the final amount of vermiculite in two ways.
There is another equation: .\(\displaystyle 4.5 + v \:=\:0.15(75 + p+v)\) [2]


Equation [1] simplifies to: .\(\displaystyle 16p - 4v \:=\:\;75\)
Equation [2] simplifies to: .\(\displaystyle 3p - 17v \:=\:\text{-}135\)

And now we can solve the system of equations.


But I'm getting some very ugly answers.
Please check my reasoning and my algebra/arithmetic.
 
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