SOLUTION: Hi A container can hold either 60 small boxes or 48 big boxes. If there are already 20 small and 24 big boxes in the container how many more big boxes can the container still hold

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Question 1207535: Hi
A container can hold either 60 small boxes or 48 big boxes. If there are already 20 small and 24 big boxes in the container how many more big boxes can the container still hold.
Found 4 solutions by ankor@dixie-net.com, greenestamps, Edwin McCravy, ikleyn:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A container can hold either 60 small boxes or 48 big boxes.
If there are already 20 small and 24 big boxes in the container how many more big boxes can the container still hold.
:
let a full box = 1
Each small box = 1/60
Each big box = 1/48
let b = no. of big boxes is can still hold
:
20%2F60 + 24%2F48 + B%2F48 = 1
convert to a common denominator of 48
16%2F48 + 24%2F48 + b%2F48 = 48%2F48
same as
16 + 24 + b = 48
b = 48-40
b = 8 more big boxes

Answer by greenestamps(13198) About Me  (Show Source):
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The fraction of the container that is filled by the 20 small boxes already in the container is 20/60 = 1/3, so 2/3 of the container is to be filled by the big boxes.

The container can hold 48 big boxes; 2/3 of 48 is 32. So for the container to be filled, there must be 32 big boxes along with the 20 small boxes.

The container currently holds 24 big boxes; the number of additional big boxes needed to fill the container is 32-24 = 8.

ANSWER: 8

Answer by Edwin McCravy(20054) About Me  (Show Source):
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Let the volume of a small box be S cubic units.
Let the volume of a big box be B cubic units.
Then the volume of the container is 60S = 48B cubic units.
Let x be the number of big boxes more the container can still hold.
The container already contains 20S+24B cubic units.
The container can hold x*B more cubic units.


60S=48B
S=expr%2848%2F60%29B
S=0.8%2AB

48B=20S%2B24B%2Bx%2AB
48%2AB=20%280.8B%29%2B24%2AB%2Bx%2AB
48%2AB=16B%2B24%2AB%2Bx%2AB
Divide through by B
48=16%2B24%2Bx
48=40%2Bx
8=x

So it'll hold 8 more big boxes.

Edwin

Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
A container can hold either 60 small boxes or 48 big boxes.
If there are already 20 small and 24 big boxes in the container
how many more big boxes can the container still hold.
~~~~~~~~~~~~~~~~~~~~~ 

20%2F60 = 1%2F3.  Hence, 1/3 of the container volume is just occupied by the 20 small boxes.


24%2F48 = 1%2F2.  Hence, 1/2 of the container volume is just occupied by the 24 big boxes.


Taking the sum, we see that 1/3 + 1/2 = 5/6 of the container volume is just occupied
by the 20 small and 24 big boxes; 1/6 of the container volume still remains free.


So, %28%281%2F6%29%29%2F%28%281%2F48%29%29 = 48%2F6 = 8 big boxes can be added to occupy free space.   ANSWER

Solved.