Using a Diagram to Find a Formula
Date: 11/13/2002 at 18:03:40 From: Kim Subject: Comparing ratio data A bag contains green, yellow and orange marbles. The ratio of green to yellow marbles is 2:5. The ratio of yellow to orange marbles is 3:4. What is the ratio of green marbles to orange marbles? I tried different formulas and I'm still not sure how to go about solving this with a formula. I did solve it by diagramming, but I know that there is a way to figure it out quicker without drawing all those marbles! My answer was 3:10. I still want a formula. Please. My daughter tried to show me but I still need help. Thanks, Kim
Date: 11/15/2002 at 00:00:26 From: Doctor Ian Subject: Re: Comparing ratio data Hi Kim, The trick is to use the diagram to _find_ an equation. If the ratio of green to yellow marbles is 2:5, then they have to come in groups of 2 and 5: (g g y y y y y) Similarly, if the ratio of yellow to orange marbles is 3:4, then they have to come in groups of 3 and 4: (y y y o o o o) Now, to compare these, you have to have some number of yellow marbles that is divisible by both 3 and 5. An easy way to do that is to multiply the first ratio by 3 to get 6:15, and the second one by 5 to get 15:20. Now we can merge the ratios: g y y o 6:15 <--> 15:20 g y o 6:15:20 So the ratio of green to orange is 6:20, which reduces to 3:10, which is what you got. (Whew!) In the general case, a:b and c:d we would do this: ac:bc <--> bc:bd ac:bc:bd so the final ratio would be ac:bd. Let's check that with your example: a = 2, b = 5, c = 3, d = 4, so the ratio should be ac:bd = 2*3:5*4 = 6:20 = 3:10 Does that make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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