Unit Analysis: Solving Word Problems

Unit Analysis can make solving complex word problems much easier.  First, DON’T BE INTIMIDATED!  The problem is not going to jump off the page and bite you if you get it wrong!  Just TRY!  Follow these basic steps to simplify problem solving.

1. What are your looking for?  Read through the problem and determine the exact units requested.

          WRITE THAT DOWN!

2. What are you given?  Sometimes, there is so much information given it is a good idea to write it all down or underline it in the problem.  It also helps if you will label what type of given information it is.  For instance:  mass, distance, …

3. Is there any other information you need?  Conversions, molar mass, reactions, …

4. Put the units together in such as way that you cancel out the units you don’t want and end up with only the units requested.  If the units are reversed in your final answer, just flip your calculation.

Example #1

A farmer has 2 cows and he decides to change to chickens.  He can barter 4 emu for each cow, 3 emu for 5 pigs, 8 pigs for 3 llama,  a llama for 20 rabbits and 3 rabbits for 2 chickens.  How many chickens can he get for both his cows?

1. What are you looking for?  chickens

2. What are you given?  Many ridiculous ratios with animals.

3. Is there any other information needed?  Not for this problem, just watch out where you step.

4. Use UA to determine the units requested.

When you plug these values into the calculator, the screen reads 66.66666667, but we are looking for WHOLE, LIVE chicken, not parts.

Remember that in science we deal with objects and measurements, NUMBERS HAVE MEANING.  You must evaluate your answer based on what the units are, as well as significant digits.

Example #2

A machine produces 4.5 x 10³ m of spaghetti noodles each minute. A package of noodles contains 128 noodles that are each 12.5 inches long.  The company sells the noodles in cartons containing 20 packages for $75.50.  If the machine runs 12.0 hr a day, 5.00 days a week, 50.0 weeks a year, how much money can the company make each year from that one machine?