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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. Tags equations, hard, involving, problem, system Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post davedave Pre-Calculus 2 June 14th, 2016 06:30 PM matisolla Calculus 2 February 27th, 2015 11:34 AM Obsessed_Math Algebra 4 February 23rd, 2012 06:03 AM fantom.1040 Algebra 2 July 2nd, 2011 06:04 AM Obsessed_Math Calculus 1 December 31st, 1969 04:00 PM

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