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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 

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
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