How Many of Each Ticket Were Sold?
Date: 09/06/2001 at 02:59:52 From: Sarah Kromer Subject: Turning a word problem into an equation Five hundred tickets were sold for a play, for $8 at the lower level and $6 at the upper level, totaling $3600. How many of each were sold? I am having trouble putting this into an equation. (8x)+ (6Y) = 500 or (8x) + (6y) = 3600 I think it is the latter but I 'm getting stuck on where to go next. I don't seem to have such a problem working out equations but when it comes to some - not all - word problems I experience a block. Please help. Thank you. Sarah
Date: 09/06/2001 at 10:49:45 From: Doctor Peterson Subject: Re: Turning a word problem into an equation Hi, Sarah. An important part of writing an equation for a word problem is to be aware of exactly what everything means. That starts with writing down explicitly what your variables mean: x = number of lower level tickets sold y = number of upper level tickets sold Now you can write expressions corresponding to particular phrases used in the problem, or to concepts implied by the problem; again, be as clear as possible: 8x = cost in dollars for all lower level tickets sold 6y = cost in dollars for all upper level tickets sold Now the total cost of ALL the tickets is the sum of these: 8x + 6y = cost in dollars of all tickets sold Now that we see just what this expression means, we know that it has to be equal to the total cost, $3600: 8x + 6y = 3600 We have one equation and two unknowns; that's not enough in general to solve the problem. But there's a piece of information we haven't used yet. Can you see how 500 = total number of tickets sold can be related to the variables x and y? That will give you a second equation; you can solve that for y, and then replace y in the first equation with the resulting expression in order to solve the problem. I hope this helps. An orderly approach can help a lot in cutting through the complexities of the English language, as well as those of math. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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