Math 8 Help - Please Help

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AbhiKap

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Hi I am in 8th grade Math and I really need help in doing some problems it is mostly related with Algebra.

The following quesiton is a mixture problem, Can you please explain how to do it. I need to know the APT method (The chart method). Please Explain.

During a science experiment, Jean created a 25% alcohol solution by mixing 7 fluid ounces of a 52% alcohol solution with a certain amount of a 4% alcohol solution. How many fluid ounces of the 25% alcohol solution did she create?

Please Answer and explain.

Thanks, Help is very much appreciated.
 
Hello, AbhiKap!

During a science experiment, Jean created a 25% alcohol solution
by mixing 7 fluid ounces of a 52% alcohol solution with a certain amount of a 4% alcohol solution.
How many fluid ounces of the 25% alcohol solution did she create?
Click to expand...

First, I'll explain the Reasoning behind the steps.
Later, I'll insert this information in a chart.

We will consider the amount of alcohol at each state.

She has 7 ounces which is 52% alcohol.
. . This contains: .\(\displaystyle (0.52)(7) \,=\,3.64\) ounces of alcohol.

She adds \(\displaystyle x\) ounces which is 4% alcohol.
. . This contains: .\(\displaystyle 0.04x\) ounces of alcohol.

Hence, the mixture contains: .\(\displaystyle 3.64 + 0.04x\) ounces of alcohol. .[1]


But we know that the mixture will be \(\displaystyle x+7\) ounces which is 25% alcohol.
. . So it contains: .\(\displaystyle 0.25(x+7)\) ounces of alcohol. .[2]


We just described the final amount of alcohol in two ways.

There is our equation! . . . . \(\displaystyle 3.64 + 0.04x \:=\:0.25(x+7)\)

Solve for \(\displaystyle x\!:\;\;3.64 + 0.04x \:=\:0.25 + 1.75\)

. . . . . . . . . . . . . . \(\displaystyle -0.21x \:=\:-1.89\)

. . . . . . . . . . . . . . . . . . .\(\displaystyle x \:=\:\frac{-1.89}{-0.21} \:=\:9 \)

Therefore, she created \(\displaystyle x+7 \,=\,16\) ounces of the 25% solution.


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


The chart looks like this:

. . \(\displaystyle \begin{array}{c|c|c|c|} & \text{ounces} & \text{percent} & \text{alcohol} \\ \hline \text{Sol'n A} & 7 & 52\% & (0.52)(7) \\ \hline \text{Sol'n B} & x & 4\% & 0.04x \\ \hline \text{Mixture} & x+7 & 25\% & 0.25(x+7) \\ \hline \end{array}\)

And the equation comes out of the last column.
 
Ounces

To know the answer to this question we need to know what exactly is 1 ounce. Once we get to know the value of 1 ounce, the calculations wil be much much easier.
1 ounce = 28.3495 gms= 30 ml

Now you can make the further calculations automatically.
 
Kaylaemarx said:
To know the answer to this question we need to know what exactly is 1 ounce. Once we get to know the value of 1 ounce, the calculations wil be much much easier.
1 ounce = 28.3495 gms= 30 ml

Now you can make the further calculations automatically.
Click to expand...

This post....never mind I'm too busy burying my face in my palm. -____-
 
Thanks Soroban, lookagain, and all the others. However, I still don't really understand these mixture problems.

Also, there are some of these that don't work with the APT and therefore have to use some other formula.

I am trying my best to understand this very complicated stuff and would like another example :

Mrs. Ferrer works in the lab at a pharmaceutical company. She needs to make 40 liters of a 19% acid solution to test a new product. Her supplier only ships a 28% and a 13% solution. Mrs. Ferrer decides to make the 19% solution by mixing the 28% solution with the 13% solution. How much of the 28% solution will Mrs. Ferrer need to use?

Soroban and the others, and example and step to step will be greatly appreciated. Thanks.
 
AbhiKap said:
Thanks Soroban, lookagain, and all the others. However, I still don't really understand these mixture problems.

Also, there are some of these that don't work with the APT and therefore have to use some other formula.

I am trying my best to understand this very complicated stuff and would like another example :

Mrs. Ferrer works in the lab at a pharmaceutical company. She needs to make 40 liters of a 19% acid solution to test a new product. Her supplier only ships a 28% and a 13% solution. Mrs. Ferrer decides to make the 19% solution by mixing the 28% solution with the 13% solution. How much of the 28% solution will Mrs. Ferrer need to use?

Soroban and the others, and example and step to step will be greatly appreciated. Thanks.
Click to expand...

There is only one principle to use - principle of conservation of "stuff".

Here you want to make 40 liters of 19% acid solution.

For that you will need (40 * 0.19 = ) 7.6 liters of acid ...............................................................(1)

Let the amount of 28% acid solution be 'x' liters. How many liters of acid is present in this solution = (0.28 * x).................(2)

Then the amount of 13% acid solution is '40 -x'. How many liters of acid is present in this solution = [0.13 * (40-x)] ............(3)

Sum of (2) and (3) gives you total acid in the mixture (conservation - assuming no reaction)

Now what ???
 
Last edited by a moderator:
Subhotosh Khan said:
There is only one principle to use - principle of conservation of "stuff".

Here you want to make 40 liters of 19% acid solution.

For that you will need (40 * 0.19 = ) 7.6 liters of acid ...............................................................(1)

Let the amount of 28% acid solution be 'x' liters. How many liters of acid is present in this solution = (0.28 * x).................(2)

Then the amount of 13% acid solution is '40 -x'. How many liters of acid is present in this solution = [0.13 * (40-..............(3)

Sum of (2) and (3) gives you total acid in the mixture (conservation - assuming no reaction)

Now what ???
Click to expand...

ok... so Now I am starting to understand. Just one question: How do you know if it is 7+x or 7-x in the amount? Thanks.
 
AbhiKap said:
ok... so Now I am starting to understand. Just one question: How do you know if it is 7+x or 7-x in the amount? Thanks.
Click to expand...
The original problem said "During a science experiment, Jean created a 25% alcohol solution by mixing 7 fluid ounces of a 52% alcohol solution with a certain amount of a 4% alcohol solution". That means you are adding liquid to the 7 oz of alchohol.
 
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