Organizing the Information in an Algebraic Word ProblemDate: 09/05/2007 at 11:31:12 From: Barbara Subject: How many games did each of these three teams win? In a baseball league of ten teams, Jennifer's team is currently in first place with forty wins. Jordan's team is eight games behind Jennifer's team. Aaron's team is eight games behind Jordan's team. In the next thirty-one games, Jordan's team won fourteen more than the number of games won by Jennifer's team. Aaron's team won sixteen less than the number of games won by Jordan's team. Three times the number of games won by Jennifer's team, during these thirty-one games, was thirty-two more than the number of games won by Aaron's. The sum of the games won by these three teams after the complete season is 153. How many games did each of these three teams win? I find the way that they are explaining it very confusing. Also I can't tell which information is necessary and which is not. I tried to make formulas to solve it but than I can't tell which information I don't need, and can't seem to make one that will give me an answer. I don't even know if a formula is the way to solving it. Date: 09/05/2007 at 16:27:29 From: Doctor Ian Subject: Re: How many games did each of these three teams win? Hi Barbara, Let's just write down what we know, and what we'd like to find out. >In a baseball league of ten teams, Jennifer's team is currently in >first place with forty wins. We can use a table to help keep things straight: Now Jennifer 40 >Jordan's team is eight games behind Jennifer's team. Now Jennifer 40 Jordan 32 >Aaron's team is eight games behind Jordan's team. Now Jennifer 40 Jordan 32 Aaron 24 >In the next thirty-one games, Jordan's team won fourteen more than >the number of games won by Jennifer's team. Let's use x to represent the number of games won by Jennifer's team: Now Later Jennifer 40 x Jordan 32 x + 14 Aaron 24 >Aaron's team won sixteen less than the number of games won by >Jordan's team. Now Later Jennifer 40 x Jordan 32 x + 14 Aaron 24 (x + 14) - 16 -> or just x - 2 >three times the number of games won by Jennifer's team, during these >thirty-one games, was thirty-two more than the number of games won by >Aaron's. What does this mean? Let's translate it, using the expressions from our table: three times the number of games won by Jennifer's team, during these thirty-one games, was thirty-two more than the number of games won by Aaron's. three times x, was thirty-two more than (x-2). 3x = (x - 2) + 32 So at this point, you have enough information to find x. >the sum of the games won by these three teams after the complete >season is 153. how many games did each of these three teams win? Once you know what x is, can you see how to find this? >I find the way that they are explaining it very confusing. Also i >can't tell which information is necessary and which is not. In general, assume something they tell you is necessary, until you know for sure that it's not. Sometimes something that seems pointless can turn out to be important later on, especially in a multi-part problem like this one. For example, I didn't really need the first column in the table to answer the first question! But it will come in pretty handy for the second. >i tried to make formulas to solve it but than i can't tell which >information i don't need, and can't seem to make one that will give >me an answer. I don't even know if a formula is the way to solving >it. It's hardly ever the case that there is a "formula" for solving a problem. That ends around 5th grade, where a typical problem will require you to do one, or maybe two, calculations to get the answer. For more complicated problems like this one, the point is to give you practice at systematically working (and thinking!) your way through problems you haven't seen before. If a formula were available, there would be no point in asking you to solve the problem. Does that make sense? Let me know if you need more help. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 09/05/2007 at 16:49:19 From: Barbara Subject: Thank you (How many games did each of these three teams win?) thank you so much for helping me.^-^ i really appreciate all your help. when you explained it i actually understood it. so thank you for working so hard to help me. you're the best! :D |
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