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Daisy and Cindy have some stickers. If Daisy gives away 6 stickers, the ratio of the number of stickers Daisy has to the number of stickers Cindy has will be 3:5. If Cindy gives away 6 stickers, the ratio of the number of stickers Daisy has to the number of stickers Cindy has will be 11:13. What is the total number of stickers they have ?

MaiaMitchell  Oct 3, 2015
 #1
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Daisy and Cindy have some stickers. If Daisy gives away 6 stickers, the ratio of the number of stickers Daisy has to the number of stickers Cindy has will be 3:5. If Cindy gives away 6 stickers, the ratio of the number of stickers Daisy has to the number of stickers Cindy has will be 11:13. What is the total number of stickers they have ?

 

Let D be the original number htat Daisy had and C be the original number that Cindy had....and we have

 

[D - 6] / [C + 6] = 3/5   

 

[D + 6] / [ C - 6]  = 11/13

 

 

Cross-multiply  in both equations

 

5[D - 6 ] =  3[C + 6]                                       13[D + 6]  = 11[C - 6]

 

5D - 30   = 3C + 18                                       13D + 78  = 11C - 66

 

5D - 3C  = 48                                                13D - 11C   =  -144

 

So we have this system

 

  5D - 3C  = 48

13D - 11C = -`144      multiply the top equation by 11 and the bottom equation by -3

 

 55D - 33C =   528

-39D + 33C  = 432     add both equations

 

16D = 960     divide both sides by 16

 

D = 60

 

And using 5D - 3C = 48  →  5(60) - 48 = 3C  →  100 - 16  = C = 84

 

So there are 60 + 84 =  144 total stickers

 

 

cool cool cool

CPhill  Oct 4, 2015

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