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# Oh dear ....

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Ivy, Ken, and Ron shared some sweets in the ratio 5: 4 : 2. Ken gave some of his sweets to Ivy and Ron. As a result, his sweets decreased by 75%. After receiving some sweets from Ken, Ron's. Find the sweets increased by 50%. Find the percentage increase in the number of sweets that Ivy had.

Apr 6, 2021

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ivy$=5k$ for some part k

ken$=4k$ for some part k

ron$=2k$ for some part k

$4k-c=0.75(4k)=3k$

$2k+c=1.5(2k)=3k$

$4k-c=3k$

$2k+c=3k$

Setting these equal, ignoring the 3k, we see $4k-c=2k+c$, so:

$4k-c=2k+c$

$2k=2c$

$k=c$.

So Ivy's sweets increased by $k$, so her percentage increase was $\frac{6}{5}=120=\boxed{20}$ percent increase

Apr 6, 2021