The Importance of Defining Variables Clearly in AlgebraDate: 11/01/2007 at 10:40:36 From: Cathy Subject: writing a formula for a word problem A sample of dimes and quarters total $18.00. If there are 111 coins in all, how many are there of each coin? I have x + y = $18.00 but I'm not sure where to go from there. Date: 11/01/2007 at 12:07:48 From: Doctor Peterson Subject: Re: writing a formula for a word problem Hi, Cathy. Before you can write an equation, you have to have a clear idea of what the variables MEAN. Are x and y supposed to be the NUMBER of dimes and the NUMBER of quarters, or the VALUE of the dimes and the VALUE of the quarters? The former is what the problem is asking for; but your equation treats them as the latter. Let's start by defining the variables: Let x = number of dimes Let y = number of quarters Now, if you knew the number of dimes, how would you calculate the VALUE of those dimes (in dollars)? Write an expression that does that calculation. Then write a similar expression for the value of the quarters. Your equation will say value of dimes + value of quarters = 18 Use your expressions to write this equation. Then you'll have to write another equation that says number of dimes + number of quarters = 111 Keeping the ideas of "number" and "value" separate is the key to solving this kind of problem. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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