SOLUTION: If a pharmacist wants to make 150 milliliters of a 20 percent alcohol solution, but only has a 30 percent alcohol solution and a 15 percent alcohol solution, how much of each solut

Question 263512: If a pharmacist wants to make 150 milliliters of a 20 percent alcohol solution, but only has a 30 percent alcohol solution and a 15 percent alcohol solution, how much of each solution should she mix together to get what she needs?
Could you please take me step by step?
Found 2 solutions by oberobic, josmiceli:
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
When solving a solution problem, you have to determine how much of the 'pure' stuff you need in the solution.
In this case, you need 150 ml of 20% alcohol.
That means there will be 30 ml of alcohol and 120 ml of water.
Using the 30% solution, how much would you need to have 30 ml of pure 'alcohol'?
30 ml = .3x
.3x = 30
x = 100 ml
That is, if you have 100 ml of 30% alcohol solution, then you have 30 ml of alcohol and 70 ml of water.
So, measure our 100 ml of the 30% alcohol solution and add 50 ml of pure water.
You now will have a total volume of 150 ml, of which, 30 ml are pure alcohol.
30/150 = .2
which means you have your required 150 ml of 20% alcohol solution.
.
Unless you're required to use the 15% alcohol solution, why bother with it at all? Just dilute the 30% solution and you're done.
.
But teachers can be picky...
.
So another way to look at the problem is to think in terms any other word problem.
You need to mix a 30% solution and a 15% solution to arrive at a 20% solution.
We know the final result is supposed to be 150 ml of 20% solution, which we can show as .2*150.
If we use 'x' amount of the 30% solution, then we are forced to use 150-x of the 15% solution.
That defines an equation:
.3x + .15(150-x) = .2(150)
.3x + 22.5 - .15x = 30
.3x - .15x = 30 - 22.5
.15x = 7.5
x = 50
So you use 50 ml of the 30% solution and 150-50 = 100 ml of the 15% solution.
Check this by determining how much 'pure stuff' is in the final solution.
.15*100 = 15
.3*50 = 15
total = 30 ml of pure alcohol in the 150 ml
.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = ml of 30% solution required
Let = ml of 15% solution required
given:
She must end up with 150 ml, so
(1)
Amount of alcohol in 150 ml of 20% solution =
ml
-----------------------------
In words:
(alcohol in 30% solution) + (alcohol in 15% solution) =
(alcohol in 20% solution)

Multiply both sides by
(2)
Multiply both sides of (1) by and
subtract from (2)
(2)
(1)

And, from (1),

50 ml of the 30% solution and 100 ml of the 15% solution
are required
check answer:
(2)
(2)

RELATED QUESTIONS
A pharmacist has 2 liters of a solution containing 30% alcohol. If he wants to have a... (answered by drk)
A pharmacist wants to prepare 300 ml of a 20 percent alcohol solution. How much of a 30... (answered by josgarithmetic,josmiceli,MathTherapy)
How many ounces of a 50 percent alcohol solution must be mixed with 80 ounces of a 20... (answered by stanbon)
A pharmacist has two solutions of alcohol, a 15% solution and a 28% solution. How many... (answered by mananth)
A scientist wants to make 6 milliliters of a 30% alcohol solution. The solution is to be... (answered by richwmiller)
a beaker contains 15 milliliters of 20% alcohol solution. how many milliliters of a 60%... (answered by checkley77)
A pharmacist has a 10% alcohol solution and a 25% alcohol solution. How many milliliters... (answered by Alan3354)
A chemist has two solutions, one is 30 percent alcohol, and the other is 90 percent... (answered by josgarithmetic)
a pharmacist wishes to prepare 30ml 0f a 20% alcohol solution. She has 30% solution and... (answered by robertb)