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**+5 **

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

CPhill
Oct 4, 2015