SOLUTION: PLEASE HELP!!!!!!!! test next class on this! A U.S nickel is composed of 3.9 grams of copper and only 1.2 grams of nickel. How many kg of copper must be combined with 4kg of nic

Question 566587: PLEASE HELP!!!!!!!! test next class on this!
A U.S nickel is composed of 3.9 grams of copper and only 1.2 grams of nickel. How many kg of copper must be combined with 4kg of nickel in the manufacture of a nickel coin?
In a town of 30,000 households, a survey was taken to estimate the number of households in which a certain TV program had been viewed. Of the 200 residences surveyed, the program had been seen in 64. Assuming that this was a representative sample, estimate the total number of households in the town in which the program was viewed.

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Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
These two problems can both be solved by using proportions. (A proportion is setting two fractions or ratios equal.)
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Let's look at the first problem. We are given that a single nickel coin contains 3.9 grams of copper and 1.2 grams of nickel. So we can set up this ratio as a copper to nickel fraction, using the weight of copper (3.9 grams) as the numerator and the corresponding weight of nickel as the denominator. In other words we set up the fractional ratio:
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Now we set this ratio equal to a second ratio. In this second ratio, we need to have the same units in the numerator as the first ratio. In the first ratio we chose to have the weight of copper in the numerator and the weight of nickel in the denominator. So our proportion will become:
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We are told that the amount of nickel to be used is 4 kg. So we substitute 4 kg in the nickel denominator of the second ratio as follows:
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Proportions can be solved by cross multiplying the numerator on one side by the denominator on the other side and setting the two products equal. In this problem we multiply the 3.9 numerator on the left side by the 4 denominator on the other side, and the resulting product of 3.9 times 4 is 15.6. Next we multiply the unknown number for copper (call it X) which is the numerator on the right side by the 1.2 denominator on the left side to get a product of 1.2X. Set the two products equal and you have:
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15.6 = 1.2X
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Solve for X by dividing both sides of this equation by 1.2. The result is:
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Doing the division on the right side you get the answer:
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And since we are relating kg to kg, the units on this answer is kg. So the answer is that X, the unknown amount of copper, must be 13 kg in order to mix with 4 kg of nickel to get the correct alloy for stamping out a bunch of nickels.
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For your second problem you are told that in 200 residences, 64 had seen the show. Set up the proportion:
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On the right side, the number of residences in the town is 30,000. Substitute this into numerator of the ratio on the right side to get the proportion:
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(Note we substituted the X for the number of residences in the town that had seen the program.)
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Cross multiply. First 200 times X = 200X. Then 30,000 times 64 = 1,920,000. Set the two products equal:
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Divide both sides by 200 to solve for X and you have:
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And doing the division on the right side results in:
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So we can say that in the town of 30,000 residences the show was seen in 9,600 of them.
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Hope this helps you to understand how you can work with proportions. Just make sure that the units of the two numerators are the same and the units of the two denominators are the same. If you do that, you don't have to worry about what should be on the top of the ratio and what is on the bottom. For example, in the first problem above we could have set up the proportion as:
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to get:
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and we would have gotten the same answer. (Note that the two cross products are still 1.2X and 15.6, the same as we got before.)
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You can try it on the second problem also.
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And you will still get the same answer of 9,600 residences in which the program was seen.
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Good luck on your test. Study hard.
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