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?
Ken buys 68 sweets.
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!!!
Thanks so much Reiny and Ajay Sir
To solve this problem, we need to break it down into steps:
Step 1: Set up the equations.
Let's assume that Jim initially had 's' sweets and 'c' chocolates. Similarly, Ken initially had 'S' sweets and 'C' chocolates.
According to the given information, Jim gave half of his chocolates to Ken, so Ken received c/2 chocolates.
Then, Ken gave half of his sweets to Jim, so Jim received S/2 sweets.
Step 2: Calculate the remaining quantities.
After the transfers, Jim has c/2 chocolates left because he did not give away any sweets.
Ken has S/2 sweets remaining because he did not give away any chocolates.
Step 3: Use the given ratios to set up equations.
The ratio of Jim's sweets to chocolates becomes 1:7, so we can set up the equation:
(S/2) / (c/2) = 1/7
The ratio of Ken's sweets to chocolates becomes 1:4, so we can set up the equation:
(S/2) / (c/2) = 1/4
Step 4: Solve the equations.
Simplify the equations:
(S/c) = 1/7 (Equation 1)
(S/c) = 1/4 (Equation 2)
Since both equations are equal to (S/c), we can set them equal to each other:
1/7 = 1/4
Cross-multiplying, we get:
4 = 7
This is not possible, and it means there is an error or inconsistency in the given information. Please double-check the question to ensure its accuracy.