How to Turn Word Problems into Algebra EquationsDate: 6/6/96 at 7:56:25 From: Anonymous Subject: Algebra word problems I am having problems setting up algebra equations from word problems. I don't know where to put the letters and numbers Could you please help? -Mike Date: 6/6/96 at 11:46:18 From: Doctor Anthony Subject: Re: Algebra word problems With word problems, you have to express the information in symbolic form, and that means you use a letter to represent some quantity that you want to find or need to use in writing down an equation. For example you could use 't' to represent time and x to represent distance. I will do a couple of examples to illustrate the method, but of course, every problem will be slightly different, and there is no ONE way of doing word problems. (1) A has three times as many sweets as B. If he gives B six sweets, he will then have twice as many as B then has. How many sweets did they each have to start with? Let x = number of sweets that B has initially; then 3x is the number that A has. If now A gives 6 sweets to B then A has 3x-6 sweets and B has x+6 sweets. Now we are told that after this transfer, A has twice as many sweets as B, so we can write down an equation to represent this fact, i.e. 3x-6 = 2(x+6) 3x-6 = 2x + 12 3x-2x = 12 + 6 x = 18 So initially B had 18 sweets and A had 3*18 = 54 sweets. Check: After transfer B has 18+6 = 24, A has 54-6 = 48, and 48 is twice 24. (2) If a man walks to the station at 3 mph he misses his train by 1 minute. If he runs at 6 mph he has 2 minutes to spare. Find the distance to the station. Let x = distance to the station. Now we know that the difference in TIME is 3 minutes between the two methods of travel, so we shall need to write down an equation involving TIME. Time = Dist/Speed, so when he walks, time = x/3 (hours) when he runs, time = x/6 (hours) Subtract these and equate to the time (in hours) between the two methods of travel. x/3 - x/6 = 3/60 x(2-1)/6 = 3/60 x/6 = 3/60 x = 18/60 x = 3/10 of a mile. So the distance to the station is 3/10 mile. You can check the result now by calculating the actual time to walk, and the time to run. Time to walk = (3/10)/3 = 1/10 hour = 6 minutes Time to run = (3/10)/6 = 1/20 hour = 3 minutes Difference = 3 minutes. You will note that the important first step is to use letters to represent unknown quantities so that you can write down equations. Lay out the work clearly, and express any information given in the question in terms of the symbols you have introduced. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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