Posted by **Mathpleasehelp** on Thursday, October 22, 2009 at 2:59am.

Jim bought some chocolates and gave half of it to Ken.Ken bought sweets and gave half of it to Jim.Jim ate 12 sweets and Ken ate 18 chocolates.The ratio of Jim's sweets to chocolate became 1:7 and the ratio of ken's sweets to chocolates became 1:4.How many sweets did Ken buy?

- Math -
**Ajay Sir**, Thursday, October 22, 2009 at 6:46am
Ken buys 68 sweets.

- Math -
**Reiny**, Thursday, October 22, 2009 at 9:04am
make a chart:

....Jim...Ken

c choc's .. s sweets

after exchange:

(1/2)s + (1/2)c ... (1/2)s + (1/2)c

after eating:

Jim eats 12 sweets , so amount left:

(1/2)s - 12 sweets and (1/2)c choc's

but that ratio is 1:7

so [(1/2)s - 12]/[(1/2)c] = 1/7

(s - 24)/c = 1/7

c = 7s - 168 #1

Ken eats 18 choc's, so amount left"

(1/2)s + (1/2)s - 18

but that ratio is 1:4

so [(1/2)s]/[(1/2)c - 18] = 1/4

s/(c-36) = 1/4

4s = c-36

c = 4s - 36 #2

equate #1 and #2 and solve for s

7s-168 = 4s+36

s = 68

back in #1 I get

c = 308

check:

Jim : 68 sweets, Ken : 308 choc's

after exchange:

Jim has 34 sweets, 154 chocs

Ken has 34 sweets, 154 chocs, they have the same

after eating as stated above

Jim has 22 sweets, 154 chocs --> ratio = 22:154 = 1:7

Ken has 34 sweets, 136 choc's --> ratio = 34:136 = 1:4

checks!!!

- Math -
**Mathpleasehelp**, Friday, October 23, 2009 at 2:14am
Thanks so much Reiny and Ajay Sir

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