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Sunday, July 23 2017 @ 09:48 PM CDT
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 Percentage question
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By: Strawberry (offline)  Sunday, September 08 2013 @ 03:07 AM CDT (Read 447 times)  
Strawberry

Catherine has a box containing some black and white counters. When she adds in 15 white counter, 65% of the counters in the box are black. If she add in another 40 black counters, 75% of the counters in the box are black. How many white counters are there in the box at first?

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By: echeewh (offline)  Sunday, September 08 2013 @ 06:32 AM CDT  
echeewh

Hey <Strawberry>

Following is my worked solution:

<when 15 W added>
B : W
65 : 35
13 : 7 -- (1)

<If another 40 B added>
B : W
75 : 25
3 : 1 -- (2)

This is a case where the number of W counters remain the same if another 40 B were added. We can then apply the <Unchanged Qty> concept here.

Multiply ratio (2) 7x.

<If another 40 B added>
B : W
21 : 7 -- (3)

Comparing ratios (1), (3):

Increase in Number of B counters
= 21u - 13u = 8u

8u --> 40
1u --> 5

Number of W counters (at first)
= 7u - 15 --> (7 × 5) - 15 = 20

===========

Trust this helps.

Do let me know again if there's further clarification.

Cheers,
Edward

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By: Strawberry (offline)  Sunday, September 08 2013 @ 12:01 PM CDT  
Strawberry

thanks for your help...

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