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Percentile problem NEED HELP
- Thread starter sydhall
- Start date
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sydhall said:How much water must be added to a bottle of 840 cm of acid which contains 10% pure acid to obtain a solution that contains 7% pure acid.
Let the amount of water = w cc
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Hello, sydhall!
Your wording is incorrect.
Since we are dealing with an amount of water, we are concerned with the water content.
We have \(\displaystyle 840\) cc of solution which is 90% water.
. . It contains: .\(\displaystyle 90\% \times 840 \,=\,756\) cc of water.
Then we add \(\displaystyle x\) cc of water.
The total amount of water in the mixture is: .\(\displaystyle x + 756\) cc.
Let's review the problem.
We start with \(\displaystyle 840\) cc of solution.
We add \(\displaystyle x\) cc of water.
The mixture contains \(\displaystyle x + 840\) cc of stuff.
The mixture is supposed to be 93% water.
. . \(\displaystyle \text{That is, it will contain: }\:0.93(x+840)\text{ cc of water.}\)
We just described the final amount of water in two ways.
There is our equation! . . . \(\displaystyle x + 756 \:=\:0.093(x + 840)\)
Can you finish it now?
Your wording is incorrect.
We have 840 cc of a solution which contains 10% acid.
How much pure water must be added to obtain a solution that contains only 7% acid?
Since we are dealing with an amount of water, we are concerned with the water content.
We have \(\displaystyle 840\) cc of solution which is 90% water.
. . It contains: .\(\displaystyle 90\% \times 840 \,=\,756\) cc of water.
Then we add \(\displaystyle x\) cc of water.
The total amount of water in the mixture is: .\(\displaystyle x + 756\) cc.
Let's review the problem.
We start with \(\displaystyle 840\) cc of solution.
We add \(\displaystyle x\) cc of water.
The mixture contains \(\displaystyle x + 840\) cc of stuff.
The mixture is supposed to be 93% water.
. . \(\displaystyle \text{That is, it will contain: }\:0.93(x+840)\text{ cc of water.}\)
We just described the final amount of water in two ways.
There is our equation! . . . \(\displaystyle x + 756 \:=\:0.093(x + 840)\)
Can you finish it now?
This is not a percentile problem. It is a mixture problem involving percents.
You might think of it this way.
First I'm wondering about the measure of cm. "cm" usually stands for centimeters which is a linear measure. I will use cc to assume you mean cubic centimeters.
You have jar containing 840 cc of a liquid that is 10% acid and 90% water. The amount of acid in this jar is .1(840) cc = 84 cc of acid.
A second jar has x cc of water which is the exact amount needed to produce the desired solution when mixed with the contents of the 1st jar. This second jar has 100% water and 0% acid.
The third jar is empty. We are going to pour all of the contents of the first jar into the third jar. Then we are going to pour the contents of the second jar (x cc) into the third jar and we will have the desired solution.
Now to set up your equation you have a couple of approaches. One approach is to build an equation based on the equality of the acid. In other words, build your equation on the basis that "The amount of acid in the first jar plus the amount of acid in the second jar equals the amount of acid in the third jar." Of course, the amount of acid in the second jar is 0 cc.
Another approach is to build your equation on the basis of the amount of water. It would be "The amount of water in the first jar plus the amount of water in the second jar equals the amount of water in the third jar."
Bear in mind that there are 840 cc of content in the first jar and x cc of content in the second jar. When these are poured into the third jar you have x+840 cc of content in the third jar.
As a hint, After you have done the pouring you will have .07(x+84) cc of acid in the third jar. Or you might want to use the fact that you have .93(x+840) cc of water in the third jar.
Good luck.
You might think of it this way.
First I'm wondering about the measure of cm. "cm" usually stands for centimeters which is a linear measure. I will use cc to assume you mean cubic centimeters.
You have jar containing 840 cc of a liquid that is 10% acid and 90% water. The amount of acid in this jar is .1(840) cc = 84 cc of acid.
A second jar has x cc of water which is the exact amount needed to produce the desired solution when mixed with the contents of the 1st jar. This second jar has 100% water and 0% acid.
The third jar is empty. We are going to pour all of the contents of the first jar into the third jar. Then we are going to pour the contents of the second jar (x cc) into the third jar and we will have the desired solution.
Now to set up your equation you have a couple of approaches. One approach is to build an equation based on the equality of the acid. In other words, build your equation on the basis that "The amount of acid in the first jar plus the amount of acid in the second jar equals the amount of acid in the third jar." Of course, the amount of acid in the second jar is 0 cc.
Another approach is to build your equation on the basis of the amount of water. It would be "The amount of water in the first jar plus the amount of water in the second jar equals the amount of water in the third jar."
Bear in mind that there are 840 cc of content in the first jar and x cc of content in the second jar. When these are poured into the third jar you have x+840 cc of content in the third jar.
As a hint, After you have done the pouring you will have .07(x+84) cc of acid in the third jar. Or you might want to use the fact that you have .93(x+840) cc of water in the third jar.
Good luck.