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?

Ajdabegano Mar 19, 2023

#1**0 **

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.**

Guest Mar 19, 2023