SOLUTION: To fill a prescription for an antibiotic, a pharmacist mixed a 50% amoxicillin concentrate with pure water to produce 200 millitliters of a 10% solution? How much water and how muc

Question 546266: To fill a prescription for an antibiotic, a pharmacist mixed a 50% amoxicillin concentrate with pure water to produce 200 millitliters of a 10% solution? How much water and how much of the concentrate did he use?
This isn't actually a homework question, but we have math exams of Thursday, and I can never remember how to do mixture problems. Thanks for the help!
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
You can find many solved problems of this type under
Homework Help Home>Word Problems>Mixtures.
For this kind of problem, you usually assume that volumes are additive, and write one equation for the volume balance and one accounting for the mass/quantity of the component of interest. You end up with a system of 2 equations to solve, but usually a pretty easy one.
Let's assume the 50% concentration for the amoxicillin concentrate is expressed as mass in volume (m/v, or w/v, grams per 100 mL).
Start with:
Let x be the volume of concentrate used in milliliters.
Let y be the volume of water added in milliliters.
Volume (or total mass) balance:
x+y=200
Amoxicillin balance (amounts in grams):
The amount/mass of amoxicillin in the volume of concentrate used is 0.50x.
The amount/mass of amoxicillin in the volume of water added (concentration=0%) is 0.00y.
The amount/mass of amoxicillin in 200ml of 10% w/v amoxicillin solution/suspension is 0.10(200).
So, 0.50x+0.00y=0.10(200).
Your problem is extra easy because you mixed your concentrate with water, rather than mixing with a more dilute formula. Your two equations are:
x+y=200 and 0.5x=20
0.5x=20 --(multiplying both sides by 2)-->x=40
Then substituting in the other equation:
40+y=200 ---(subtracting 40 from both sides)---> y=200-40=160
Mix 40 mL of concentrate with 160 mL water to get your 10% amoxicillin.
RELATED QUESTIONS
I need help setting up this problem. A prescription requires a cough syrup to contain... (answered by mananth)

How many liters of pure water should be mixed with an 8-L solution of 60% acid to produce (answered by stanbon,richwmiller)

A fruit drink concentrate is 15% water. How many liters of pure water should be added to... (answered by richwmiller)

An 80% fruit juice concentrate is to be mixed with water to produce 10 gallons of a 20%... (answered by josgarithmetic)

Howw many liters of pure water should be mixed with a 5L solution of 50% acid to produce... (answered by josgarithmetic)

How many liters of pure water should be mixed with a 9-L solution of 90% acid to produce... (answered by richwmiller)

How many liters of pure water should be mixed with a 2L solution of 70% acid to produce a (answered by josgarithmetic,solver91311)

A 12-ounce can of frozen orange juice concentrate is mixed with 3 cans of cold water to... (answered by stanbon,edjones)

A 12 ounce can of frozen orange juice concentrate is mixed with 3 cans of cold water to... (answered by scott8148)