Question 1201235: Hi
Bob and Jill had some sweets. After Jill gave Bob 20% of what she had Bob would have 60% more than Jill. What percentage of his total number of sweets must Bob give to Jill so that they will have the same number of sweets.
Thanks
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let b = the number of sweets that bob had.
let j = the number of sweets that jill had.
After Jill gave Bob 20% of what she had, Bob would have 60% more than Jill.
assume jill had x number of sweets.
after she gave 20% of them to bob, she would have had .8x number of sweets left.
after jill gave 20% of her sweets to bob, bob would have had 1.6 * the number of sweets that jill had left.
bob would have had 1.6 * .8 * x = 1.28 * x sweets.
after the transaction:
bob had 1.28 * x number of sweets.
jill had .8 * x number of sweets.
you want to know what percentage of sweets that bob had were given to jill so that they both have the same number of sweets.
let that quantity be equal to y.
you get 1.28 * x - y = .8 * x + y
add y to both sides of this equation and subtract .8 * x from both sides of this equation to get:
1.28 * x - .8 * x = 2 * y
simplify to get:
.48 * x = 2 * y
solve for y to get:
y = .48 / 2 = .24 * x
replace y with .24 * x in the equation of 1.28 * x - y = .8 * x + y.
the equation becomes:
1.28 * x - .24 * x = .8 * x + .24 * x
simplify to get:
1.04 * x = 1.04 * x
the ratio of .24 * x to 1.28 * x is equal to (.24 * x) / (1.28 * x) = .1875.
this suggest that bob would have had to give 18.75% of what he had to jill so that they would both have the same amount.
to see if this makes sense, let x = any random number that makes some kind of sense.
i let x = 1000
that's the amount that jill had to start with.
she gave 20% of that to bob
bob would then have had 1.6 * what jill had left.
jill would have had 800 left.
bob would have had 1280, because 1.6 * 800 = 1280.
bob would then have had to give 18.75% of that to jill so that they would both have the same amount.
.1875 * 1280 = 240.
bob gave 240 to jill.
bob now has 1280 - 240 = 1040.
jill now has 800 + 240 = 1040.
they both now have the same amount.
it looks like your solution is that bob would have had to give 18.75% of his sweets to jill so that they would both have the same number of sweets.
Answer by MathTherapy(10557)  (Show Source):
You can put this solution on YOUR website!
Hi
Bob and Jill had some sweets. After Jill gave Bob 20% of what she had Bob would have 60% more than Jill. What percentage of his total number of sweets must Bob give to Jill so that they will have the same number of sweets.
Thanks
Let original amount Jill had, be J
After giving Bob 20% (.2J), she had 80%, or .8J remaining
Since after getting 20% of Jill's, Bob had 60% MORE than Jill, Bob's amount then was 1.6(.8J) = 1.28J
Let amount to be given by Bob to Jill, so they'll have the same amount, be a
After giving "a" to Jill, Bob will have 1.28J - a remaining, while Jill will
have .8J + a. Since they will have the same amount then, we get: 1.28J - a = .8J + a
- a - a = .8J - 1.28J
- 2a = - .48J
Amount to be given by Bob to Jill, so they'll have the same amount, or 
Percent of Bob's amount to be given to Jill, so they'll have the same amount: 
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