My Math Forum a hard problem involving a system of equations

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 June 15th, 2016, 12:13 AM #1 Senior Member   Joined: Apr 2008 Posts: 194 Thanks: 3 a hard problem involving a system of equations I am going to write down a problem. Tom is going to mix Chemical A and Chemical B in his lab. He wants to make an 800ml mixture with 61% of acid. Chemical A has 40% of acid and Chemical B has 75% of acid. (a) What volume of each chemical does he need? (b) What is the maximum volume of a mixture he can make with the two chemicals? (a) This is how I set up the equations. A + B = 800 0.4A + 0.75B = (800)(0.61) Solving them gives A = 320ml and B = 480ml. I checked the answer key and got part (a) right, but I cannot do part (b). The answer is 1666ml. I don't know how to get this answer. Can someone explain it? Thanks a lot.
 June 15th, 2016, 03:13 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Unless that is additional information (how much of chemical A and chemical B are available) it is impossible to say what the maximum amount of mixture is.
 June 19th, 2016, 11:37 PM #3 Senior Member   Joined: Apr 2008 Posts: 194 Thanks: 3 I am sorry about the ambiguity. I found the exact wording of the problem. This is how it goes. (ex) A scientist has to make 800 ml of 61% sulfuric acid solution using a 1 litre bottle of 40% sulfuric acid solution and a 1 litre bottle of 75% sulfuric acid solution. (b) What is the maximum volume, rounded down to the nearest ml of 61% sulfuric acid solution which the scientist could mix with the original bottles of solutions? The answer is 1666ml. I solved part (a) in the original post. I can't do part (b). Can someone explain it? Thanks a lot.
 June 20th, 2016, 03:19 AM #4 Math Team     Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1588 In part (a), you came up with 320 mL of A and 480 mL of B. Max volume would use the entire 1 L = 1000 mL of B because it requires the largest amount. 320/480 = 2/3 ratio of A to B 2/3 = A/1000 A = 2000/3 = 666.666... Add that amount of A to the 1000 mL of B Thanks from davedave
 June 23rd, 2016, 02:33 AM #5 Senior Member   Joined: Apr 2008 Posts: 194 Thanks: 3 Thanks skeeter.

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