SOLUTION: I've seen some pretty hardcore problems answered here so I apologize if I waste your time with this one, but I don't remember how to solve these at all :/ A pharmacist has one s

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Question 206874: I've seen some pretty hardcore problems answered here so I apologize if I waste your time with this one, but I don't remember how to solve these at all :/
A pharmacist has one solution that is 20% HCI and another solution that is 80% HCI. How much of the 80% solution must be added to 10cm³ of the 20% solution to make a solution that is 60% HCI?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let
x = volume of the first solution (in cubic centimeters)
y = volume of the mixed solution. In other words, the volume of the combination of the two volumes of the 'x' and 10 cubic centimeter solutions. (note: volume is again in cubic centimeters)



Since 'y' is the combination of the first two solutions, this means that y=x%2B10


To find the second equation, this is where things get a bit tricky. There are 'x' cubic centimeters of the 80% solution (of HCI). So this means that there are 0.8x cubic centimeters of pure HCI in the first solution. Likewise, in the second solution, there are 10 cubic centimeters. Since the second solution is 20% HCI, this tells us that there is 0.2(10) cubic centimeters of pure HCI in the second solution. Now since we want the final solution to be 60% HCI, this means we're going to set the sum of 0.8x and 0.2(10) equal to 0.6y (since 0.6y is also pure HCI).


In other words, we're going to have this second equation: 0.8x%2B0.2%2810%29=0.6y


0.8x%2B0.2%2810%29=0.6y Start with the given equation.


0.8x%2B0.2%2810%29=0.6%28x%2B10%29 Plug in y=x%2B10 (the first equation)


0.8x%2B0.2%2810%29=0.6x%2B0.6%2810%29 Distribute


0.8x%2B2=0.6x%2B6 Multiply


8x%2B20=6x%2B60 Multiply EVERY term by 10 to move the decimal points one spot to the right. This will make every value a whole number.


8x=6x%2B60-20 Subtract 20 from both sides.


8x-6x=60-20 Subtract 6x from both sides.


2x=60-20 Combine like terms on the left side.


2x=40 Combine like terms on the right side.


x=%2840%29%2F%282%29 Divide both sides by 2 to isolate x.


x=20 Reduce.


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Answer:

So the solution is x=20


This means that 20 cubic centimeters of the first solution (that is 80% HCI) is needed.