Instead of dividing 391 cookies among 3 child | vedclass

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(C) The actual ratio is $\frac{1}{5}: \frac{1}{4}: \frac{1}{8}$. To simplify,multiply by the $LCM$ of $5, 4, 8$,which is $40$. The ratio becomes $8: 1

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$C, 99$ cookies

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(C) The actual ratio is $\frac{1}{5}: \frac{1}{4}: \frac{1}{8}$. To simplify,multiply by the $LCM$ of $5, 4, 8$,which is $40$. The ratio becomes $8: 10: 5$. The sum of the ratio parts is $8 + 10 + 5 = 23$.Actual shares:$A = \frac{8}{23} 	imes 391 = 136$$B = \frac{10}{23} 	imes 391 = 170$$C = \frac{5}{23} 	imes 391 = 85$The cookies were actually divided in the ratio $5: 4: 8$. The sum of the ratio parts is $5 + 4 + 8 = 17$.New shares:$A = \frac{5}{17} 	imes 391 = 115$$B = \frac{4}{17} 	imes 391 = 92$$C = \frac{8}{17} 	imes 391 = 184$Comparing the gains:$A$ gains: $115 - 136 = -21$ (Loss)$B$ gains: $92 - 170 = -78$ (Loss)$C$ gains: $184 - 85 = 99$ (Gain)Therefore,$C$ gains the most,which is $99$ cookies.

Instead of dividing $391$ cookies among $3$ children $A, B, C$ in the ratio $\frac{1}{5}: \frac{1}{4}: \frac{1}{8}$,they were divided in the ratio $5: 4: 8$. Who gains the most and how many?

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