SOLUTION: Kathy has 5 liters of 32% acid solution and she also has a large amount of a 26% acid solution. How many liters of the 26% solution can Kathy mix with the 5 liters of 32% solution

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Question 197810: Kathy has 5 liters of 32% acid solution and she also has a large amount of a 26% acid solution. How many liters of the 26% solution can Kathy mix with the 5 liters of 32% solution in order to produce a 50% acid solution? I know that there is no solution due to the fact that combining solutions of 26% and 32% will never create a solution of greater concentration then 32% however I need to know how to set up the system of equations to solve this problem regardless of the outcome. What are the two equations?

Answer by stanbon(75887) (Show Source):
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Kathy has 5 litres of 32% acid solution and she also has a large amount of a 26% acid solution. How many liters of the 26% solution can Kathy mix with the 5 liters of 32% solution in order to produce a 50% acid solution? I know that there is no solution due to the fact that combining solutions of 26% and 32% will never create a solution of greater concentration then 32% however I need to know how to set up the system of equations to solve this problem regardless of the outcome. What are the two equations?
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Quantity Equation:
lNumber of litres:
y = x + 5
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Quality Equation:
acid + acid = acid
0.32*5 + 0.26x = 0.50y
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Cheers,
Stan H.