Orange and Grape SodasDate: 08/24/2002 at 10:17:40 From: Dustin Subject: Guess and check problem Douglas bought a total of 50 cans of orange and grape sodas. He bought 12 more cans of grape than orange. How many of each did he buy? I have subtracted, added, and multiplied, and still can't get the answer. Would appreciate your help. Thanks. Dustin Date: 08/24/2002 at 10:58:21 From: Doctor Sarah Subject: Re: Guess and check problem Hi Dustin - thanks for writing to Dr. Math. Are you allowed to use a little algebra? You could let the cans of orange soda equal x. Then the cans of grape soda will be x+12, and the total will be 50: x + x + 12 = 50 Collect like terms (the x's): 2x + 12 = 50 Subtract 12 from both sides of the equation: 2x = 38 Divide both sides of the equation by 2: x = 19 (number of cans of orange soda) x + 12 = 31 (number of cans of grape soda) Does 19 + 31 equal 50? - Doctor Sarah, The Math Forum http://mathforum.org/dr.math/ Date: 08/25/2002 at 15:33:46 From: Doctor Greenie Subject: Re: Guess and check problem Hi, Dustin - Your question and the answer provided by Dr. Sarah interested me. Her response was perfectly correct and appropriate - if you are allowed to use algebra. However, it appears likely to me that, if you are really 11 years old, then you aren't expected to use algebra in the solution of the problem. Here is another approach to the problem which you can use to get the answer without using algebra: The problem says Douglas bought 12 more cans of grape soda than of orange, and that he bought a total of 50 cans of soda. Suppose, for the moment, we "take away" those 12 extra cans of grape soda from the problem - what do we have then? Now, without those 12 "extra" cans of grape soda, he has bought the same number of cans of orange and grape sodas, and he has bought a total of 38 cans (50 - 12) of soda. That means he has bought 19 (half of 38) cans of each type of soda. Now we add those 12 extra cans of grape soda back into the problem and find that he bought 19 cans of orange soda and 31 cans (19 + 12) of grape soda. If you haven't yet started to learn any algebra, it might be interesting to compare my response to the one provided earlier by Doctor Sarah. You might see that the path to the solution using the formal algebra of her approach and the logical reasoning of my approach are in fact virtually identical - hers just uses the formal algebraic notation, while mine is more informal. Comparing the two responses, you might be able to see how algebra is used to solve problems like this in a formal manner. - Doctor Greenie, The Math Forum http://mathforum.org/dr.math/ Date: 08/26/2002 at 15:13:34 From: Dustin Subject: Thank you (Guess and check problem) Dr. Greenie, Thank you so much for your answer on the sodas. I really appreciate it. This makes more sense than the other way. I don't think I should be having algebra either in the 6th grade. Maybe this will help me. Thanks again, Dustin |
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