My Math Forum how many mL of 75% alcohol is needed?

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 June 11th, 2018, 07:28 PM #1 Member   Joined: May 2015 From: Australia Posts: 77 Thanks: 7 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.
 June 11th, 2018, 09:07 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,039 Thanks: 1063 How are you going to add 75% alcohol to 1000mL and end up with 500 mL?
 June 11th, 2018, 09:23 PM #3 Member   Joined: May 2015 From: Australia Posts: 77 Thanks: 7 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?
 June 12th, 2018, 01:18 AM #4 Member   Joined: May 2015 From: Australia Posts: 77 Thanks: 7 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.
 June 12th, 2018, 01:41 AM #5 Global Moderator   Joined: Dec 2006 Posts: 19,291 Thanks: 1683 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.
 June 12th, 2018, 02:57 AM #6 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,904 Thanks: 883 Code: QUANTITY PERCENTAGE a u b v === === a+b w? w = (au + bv) / (a + b)

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