vkay Posted October 8, 2009 Share Posted October 8, 2009 I have the answer, I just can't get there myself. I'm just not functioning upstairs today for some reason.... Abe, Barry, and Carlos have 256 marbles altogether. The ratio of Abe's marbles to Barry's marbles is 4:3. Barry has 14 more marbles than Carlos. How many marbles does Abe have? The answer should be 108. What would be the mathematical way to approach this? Quote Link to comment Share on other sites More sharing options...
Miss Marple Posted October 8, 2009 Share Posted October 8, 2009 Here's how you can do it mathematically: Abe + Barry + Carlos = 256 Carlos = Barry -14 So by substitution: Abe + Barry + (Barry - 14) = 256 Abe + Barry + Barry = 270 Assigning X as the value of each part: 4X + 3X + 3X = 270 10X = 270 X = 27 Abe is 4X so he has 27 x 4 = 108 marbles Quote Link to comment Share on other sites More sharing options...
vkay Posted October 8, 2009 Author Share Posted October 8, 2009 Here's how you can do it mathematically: Abe + Barry + Carlos = 256 Carlos = Barry -14 So by substitution: Abe + Barry + (Barry - 14) = 256 Abe + Barry + Barry = 270 Assigning X as the value of each part: 4X + 3X + 3X = 270 10X = 270 X = 27 Abe is 4X so he has 27 x 4 = 108 marbles This is so much more straight forward than what was going on in my head. I was trying to approach it like this: Carlos has X amount, Barry has X+14, and Abe has 4/3(X+14) So something like: 4/3(X+14) + (X+14) = X = 256 Then with a lot of messing around, it gets there, but I knew it was more complicated than it had to be. Thanks for your help. :D:D:D Quote Link to comment Share on other sites More sharing options...
Georgia Posted October 8, 2009 Share Posted October 8, 2009 Here's a bar diagram method much the same as previous post: Draw 3 bars, divided into sections (per the ratio) as follows (I'll use X's) Abe X X X X Barry X X X Carlos (Barry's bar minus 14) If you add 14 to Carlos' bar (to make his equal to Barry's), you'll have 3 sections for Carlos and add 14 to 256 = 270. You now have 10 sections (Abe=4, Barry=3, Carlos=3) and 270 total. 270 divided by 10 = 27 per section, then just multiply by the number of sections in the bar for Abe (4). It's hard to explain bar diagrams with words! But I love them. Quote Link to comment Share on other sites More sharing options...
Miss Marple Posted October 8, 2009 Share Posted October 8, 2009 You're welcome! And it gave me a nice problem to have the boys work for some additional practice :) Quote Link to comment Share on other sites More sharing options...
Mom2GirlsTX Posted October 8, 2009 Share Posted October 8, 2009 And this is why I love this board! I read the problem, then saw Cynthia's explanation and a little light went off in my head and I understood it. I just love this board. :D Quote Link to comment Share on other sites More sharing options...
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