8filltheheart Posted November 7, 2012 Share Posted November 7, 2012 In my dd's geo bk, they are covering a section on ratios. The question reads: 2 numbers a and b are in the ratio 3:4. If the first number is decreased by 2 and the second is decreased by 1, they are in the ratio 2:3. Find a and b. Dd worked the problem similar to the way as the answer key. I didn't. :tongue_smilie: We both got the same answer, but I got my answer in a couple of seconds, whereas their approach is much longer. I am wondering if there is a reason not to work the problem the way I did, b/c I certainly don't want to confuse dd. So......here is the answer key's answer: a/b=3/4 4a=3b 4a-3b=0 (a-2)/(b-1)=2/3 (then all the steps cross multiplying) 3b-2b=4 Then by solving via simultaneous equations: 4a-3b=0 3a-2b=4, a=12 b=16 When I solved the problem, I thought way more simply. I knew that the numbers were a ratio, so I thought in terms of 3x/4x So I simply did (3x-2)/(4x-1)= 2/3 and solved for x and got x=4, so the ratio is 12/16 Am I missing something? Is there a reason not to solve the problem the way I did? Thanks! Quote Link to comment Share on other sites More sharing options...
regentrude Posted November 7, 2012 Share Posted November 7, 2012 There is really not much difference - except that you introduced a new variable x and did several steps in your head instead of writing them out individually. A strong math student will have no trouble understanding your approach which looks more elegant. A struggling math student, however, would benefit from setting it up more slowly and NOT introducing yet another variable x - the main difficulty for students is operating with variables, and solving it in terms of the original variables a and b is preferable from a didactic point of view. You know what type of student your DD is and whether seeing a more elegant solution would cause delight or confusion. Quote Link to comment Share on other sites More sharing options...
8filltheheart Posted November 7, 2012 Author Share Posted November 7, 2012 Thanks, Regentrude. I was pretty sure there was no reason not to do it my way, but I wanted to make sure. Quote Link to comment Share on other sites More sharing options...
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