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Proportions and Unknown multiplier problem

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by gmattesttaker2 » Thu Jul 05, 2012 11:03 pm
Hello,

This is from MGMAT Guide 1 (5th edition):

Alexandra needs to mix cleaning solution in the following ratio: 1 part bleach for every 4 parts water. When mixing the solution, Alexandra makes a mistake and mixes in half as much bleach as she ought to have. The total solution consists of 27 ml. How much bleach did Alexandra put into the solution?

Answer given is 3 ml


Any suggestions on how to solve this problem? Thanks a lot.

Best Regards,
Sri
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by eagleeye » Fri Jul 06, 2012 3:16 am
For the proper ratio, we need:

1 part bleach: 4 parts water = 1:4
If only half of bleach is put in, the ratio becomes
1/2 : 4 = 1:8

Let amount of bleach that Alexandra put in the solution is x. Then amount of water = 8x.
Now total amount = x+8x = 9x.
We are given that 9x=27 => x=3.
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by Bill@VeritasPrep » Fri Jul 06, 2012 5:40 pm
eagleeye wrote:For the proper ratio, we need:

1 part bleach: 4 parts water = 1:4
If only half of bleach is put in, the ratio becomes
1/2 : 4 = 1:8

Let amount of bleach that Alexandra put in the solution is x. Then amount of water = 8x.
Now total amount = x+8x = 9x.
We are given that 9x=27 => x=3.
This is the best approach. Take the original ratio, apply the change given (half as much bleach), and then incorporate the actual amount (27 mL).
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by windchaser » Mon Jul 09, 2012 12:15 am
This is my approach:
original ratio is 1:4
half as much as she ought to have, means it is now 0.5 : 4
27/4.5= 6
6*0.5 = 3mL
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