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Calculus/Mixture problems

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Question
1. Joe created a metal containing 40% platinum by combining two other metals. One of these other metals weighed 12 lb. and contained 45% platinum. If the other weighed 3 lb. then what percent of it was platinum?
2. 12 gal. of a saline solution was mixed with 3 gal. of a 30% saline solution to make a 38% saline solution. Find the percent concentration of the first solution.
3. 9 ml of a 20% alcohol was mixed with 6 ml of pure water. Find the concentration of the new mixture.
4. How much clay do you need to add to 8m^3 of soil with 30% clay in order to make a soil with 60%?
5. 9 L of an alcohol solution was mixed with 1L of a 80% alcohol solution. Find the percent concentration of the first solution. PLEASE HELP! I also have to show the equation. Thanks

Answer
Questioner:Kimberly
Country:Georgia, United States
Category:Calculus
Private:No
Subject:Pre-Calculus Algebra
Question:
1. Joe created a metal containing 40% platinum by combining two other metals. One of these other metals weighed 12 lb. and contained 45% platinum. If the other weighed 3 lb. then what percent of it was platinum?
--------------------------------------------------------
This is referred to as a percent-mixture problem, (but see comment at the end) and you organize it with a table:
(View it in a fixed-size font, such as courier)

   Stuff          | Amount | percent | Pure Pt|
-------------------+--------+---------+--------+
First metal        |  12    |   .45   |12(.45) |
-------------------+--------+---------+--------+
Second metal       |   3    |    p    |   3p   |
-------------------+--------+---------+--------+
Metal created      |   15   |   .40   | ?????? |
-------------------+--------+---------+--------+
Key ideas:

1. The amounts add up.

2. The entries in the Pure Pt column are obtained by multiplying.

3. By putting “p” in the center spot you state that “p’ stands for the percent concentation of the second metal.  (Remember, your teacher told you to say what your variable stands for -- this is how you do it.)

4. The amounts add up. Oh, I said that.  But this time I mean it – the amounts of pure Pt add up, too.

That gives you the equation – the ?????? entry is obtained by EITHER addition or multiplication.

12(.45) + 3p = 15(.40)

Take it from there.
..............................................
2. 12 gal. of a saline solution was mixed with 3 gal. of a 30% saline solution to make a 38% saline solution. Find the percent concentration of the first solution.
3. 9 ml of a 20% alcohol was mixed with 6 ml of pure water. Find the concentration of the new mixture.
4. How much clay do you need to add to 8m^3 of soil with 30% clay in order to make a soil with 60%?
5. 9 L of an alcohol solution was mixed with 1L of a 80% alcohol solution. Find the percent concentration of the first solution. PLEASE HELP! I also have to show the equation. Thanks
.........................................
Comments:
1.The others should work out the same way. I’ll leave them to you.
2.This is NOT calculus; this is not precalculus; this is elementary algebra.

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