posted by 6th grade .
Jim bought some chocolatees and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim.Jim ate 12 sweets and ken ate 18 chocolates.The ratio of Jim's sweets to chocolates became 1:7 and the ratio of Ken's sweets to chocolates became 1:4. How many sweets did ken buy?
Jim and Ken have the same number of sweets and chocolates to begin with, as each of them gave half to the other. So:
From Jim eating 12 sweets, we can conclude that S-12=7C, as the number of sweets he has after eating 12 is seven times the number of chocolates he has.
From Ken eating 18 chocolates, we can conclude that S=4(C-18) or S=4C-72.
We can substitute the equation from Ken into the Jim equation, getting 4C-72-12=7C. -84=3C. C=-28, so S=-192. Ken originally had 2S sweets, so Ken bought -384 sweets. Check to see if you have accurately written this problem down, as the answer seems suspect.