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...
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