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The ratio of the number of biscuits in Container H to the number of biscuits in Container J was 5 : 3. 20% of the biscuits in Container H and 0.6 of those in Container J were round. After transferring the biscuits between the 2 containers, the number of square biscuits in both containers are the same. Likewise, the number of round biscuits in both containers are the same. If a total of 162 of biscuits were moved, how many more biscuits were there in Container H than Container J at first?

 Mar 19, 2023
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H/J ==5/3...................................(1)
0.20H ==round
0.60J ==round
R==Number of round biscuits transferred.
0.20H + R==0.60J - R..............(2)
S==Number of square biscuits transferred.
0.80H==square
0.40J==square
0.80H - S ==0.40J + S.............(3)
R  +  S ==162............................(4), solve for H, J, R, S

 


Using the above 4 equations with substitutions and eliminations we get:
H==450 - original number of biscuits
J== 270 - original number of biscuits
R==36 -  round biscuits transferred from J to H
S ==126 - square biscuits transferred from H to J

 


450 + 36 - 126 ==360 biscuits in H after the transfer.
270 - 36 + 126 ==360 biscuits in J after the transfer.
H - J ==450 - 270 ==180 - extra number of biscuits that were in container H than container J at first.

 Mar 19, 2023

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