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June 15th, 2016, 12:13 AM   #1
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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.
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June 15th, 2016, 03:13 AM   #2
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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.
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June 19th, 2016, 11:37 PM   #3
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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.
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June 20th, 2016, 03:19 AM   #4
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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
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June 23rd, 2016, 02:33 AM   #5
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Thanks skeeter.
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