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June 11th, 2018, 07:28 PM   #1
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how many mL of 75% alcohol is needed?

How many mL of 75% alcohol should be mixed with 10% of 1000 cc alcohol to prepare 30% of 500mL alcohol solution?
a) 346.16mL
b) 234.43mL
c)153.84mL
d) 121.12mL
Answer: C (153.84mL)

I got an answer of 66.67mL for some reason. this is how I thought the solution should be:

Need: how many mL of 75% alcohol
Have: 1000mL of 10% alcohol = 100mL alcohol in 1000mL
500mL of 30% alcohol = 150mL alcohol in 500mL
So we need 150mL - 100mL = 50mL alcohol
Volume * 75% = 50mL
Volume = 50mL/0.75 = 66.67mL

I'm not sure where I went wrong in my solution

Last edited by skipjack; June 12th, 2018 at 01:15 AM.
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June 11th, 2018, 09:07 PM   #2
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How are you going to add 75% alcohol to 1000mL and end up with 500 mL?
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June 11th, 2018, 09:23 PM   #3
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So my logic to solving this question comes from the fact that I found a similar question from last year's studies.

Last year's question is below (maybe it can help with solving the first question):

What volume of ethanol (96% v/v) should be added to 500mL of 70% (v/v) ethanol such that when the mixture is made to 2.5L with water, the final concentration of ethanol is 55% (v/v)?
Answer = 1067.6mL


The solution:
500mL of 70% v/v = 70mL/100mL = 350mL in 500mL
2.5 L of 55% v/v = 55mL/100mL = 1375mL in 2500mL
we need: 1375 - 350 = 1025mL
Volume x 96% = 1025
Volume = 1025/0.96 = 1067.7mL

I'm pretty both types of questions are very similar to each other. So does this mean the first question has an error?
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June 12th, 2018, 01:18 AM   #4
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I just asked my friend how she worked it out, and she sent me this:

75-10 = 65
30-10 = 20
500 x (20/65) = 153.84mL

I'm not sure if the logic is right though.
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June 12th, 2018, 01:41 AM   #5
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Your wording is a bit odd, so I'll just show you a way to get answer (C).

Let's assume that you mix x ml of a liquid that is 75% (i.e., 3/4) alcohol with (500 - x) ml of a liquid that is 10% (i.e., 1/10) alcohol, so that the mixture's volume is 500ml.

The volume of alcohol in the mixture is ((3/4)x + (1/10)(500 - x)) ml, and you want this volume to be 30% of 500 ml, which is 150 ml.

You therefore need to solve (3/4)x + (1/10)(500 - x) = 150.

Isolating x gives the equation (3/4 - 1/10)x = 150 - 500/10 = 100.

Multiplying that equation by 20 gives 13x = 2000, so x = 2000/13, which is in agreement with choice (C).

Note that if we start by multiplying by 100, we are solving 75x + 10(500 - x) = 30*500,
which is equivalent to (75 - 10)x = (30 - 10)500. Hence your friend's working was correct. When you've done this type of calculation a few times, you know exactly what to do to get the answer quickly.
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June 12th, 2018, 02:57 AM   #6
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Code:
QUANTITY  PERCENTAGE
      a               u
      b               v
  ===           ===
   a+b              w?
w = (au + bv) / (a + b)
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