Solving a Ratio ProblemDate: 02/06/2006 at 20:21:39 From: Jennifer Subject: How do you solve a ratio? There are 33 red and yellow counters in a container. The ratio of red to yellow is 3 to 8. How many red and yellow counters are there? I know there are 33 and that for every three red there are eight yellow. Date: 02/06/2006 at 22:08:44 From: Doctor George Subject: Re: How do you solve a ratio? Hi Jennifer, Thanks for writing to Doctor Math. I'll show you two ways to think about this problem, one using algebra and one without it. One of my high school teachers showed me a clever way to solve this problem using algebra. If we use R and Y for the number of red and yellow counters then let R = 3x Y = 8x for some unknown value x. We can see immediately that R/Y has the correct ratio of 3/8. Now find the sum. R + Y = 33 Can you finish it from here? When you take the next step you should see the reason for introducing the new variable x. Another way to think about this, which is very similar but doesn't use the variable, is to think about groups of the counters. You know that for every 3 red there are 8 yellow, so together that would make a group of 11 counters. How many of those groups of 11 are there if there are 33 counters in the container? Can you use that information to figure out how many of each color there are? Write again if you need more help. - Doctor George, The Math Forum http://mathforum.org/dr.math/ |
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