Using Tables to Tame a Problem
Date: 09/19/2003 at 03:05:30 From: Tiffany Subject: Math Problem The Ride-A-Mile bicycle company presented their new models at a bike show. Racing models were either silver or blue. Every silver bike was a racing model. 1/2 of the blue bikes were racing models. 1/3 of the bikes were racing models. There were 40 blue bikes and 30 silver bikes. How many bicycles were neither blue nor silver? I find the fractions especially confusing.
Date: 09/19/2003 at 16:47:43 From: Doctor Peterson Subject: Re: Math Problem Hi, Tiffany. The hard part, I think, is to make sense of all the information and find an orderly way to think about it. Maybe we can start by listing the different categories of bikes there are: bikes can be racing, or non-racing bikes can be blue, silver, or another color Now maybe we can make a table: racing non +-------------- blue | silver | other | Now we can start to fill in information. We know that ALL racing bikes are either silver or blue, so we can put a 0 in the space for other colors: racing non +-------------- blue | silver | other | 0 We know that ALL silver bikes are racing bikes: racing non +-------------- blue | silver | 0 other | 0 We know only that half of the blue bikes are racing bikes, so that doesn't give us a number to fill in for blue, but we can note the fact that the two numbers beside blue will be equal. Similarly, we know that 1/3 of ALL bikes are racing bikes. Keep note of that. We may want to make a row for total number of bikes of each type. racing non +-------------- blue | silver | 0 other | 0 +-------------- total | Now we have totals of blue and silver bikes, so we can add a total column: racing non total +--------------+----- blue | | 40 silver | 0 | 30 other | 0 | +--------------+----- total | | Now, can you take over from here? We have to finish filling in numbers, using the facts we wrote down but haven't used yet. If you need more help, please write back and show me how far you got. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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