How Much to Add?
Date: 01/16/98 at 09:08:52 From: Curt Culbertson Subject: Fourth substance In Chemistry class Tonya measured 215 MG of substance A, 423 MG of substance B, and 189 MG of substance C into a container. She must add enough of a fourth substance to make the entire mixture weigh 2.5 grams. How much of the fourth substance should she add?
Date: 01/19/98 at 10:50:01 From: Doctor Trone Subject: Re: Fourth substance Dear Curt, This is a very interesting question. The first thing you should notice about the problem is that the units are not the same. To solve this problem all the units have to be in milligrams or in grams. Let's say you want to change all the units into milligrams. The prefix milli- means 1 part out of 1000 or 1/1000 or .001. In other words, one milligram is .001 grams. Our task is to change 2.5 grams into milligrams. It is simple to do, just multiply 2.5 grams times 1000 because there are 1000 milligrams in one gram. Thus, 2.5 grams is really the same as 2500 milligrams. Now the problem looks like this: 215 mg + 424 mg + 189 mg + ? = 2,500 mg We need to find the mass of the fourth substance (?). This equation is like solving an equation with smaller numbers. Suppose you were asked to solve this equation: 2 + 3 + 4 + ? = 20 You can use mental arithmetic to arrive at 11, but when numbers get large, we need to use another method. One way is to add what we know: 2 + 3 + 4, which equals 9. Thus, we have 9 + ? = 20. Using fact families, we can get 20 - 9 = ? or 11. So we really have a subtraction problem. Getting back to your problem: add up what you have and subtract from the 2,500 mg. Your answer will be in milligrams. How would you get your answer in grams? Let me know if I can be of more assistance, and have fun doing math. -Doctor Trone, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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