Problem Solving

When we have a mixtures problem like this, building equations is a great route.

Total volume of medication: a + b = 750
Total volume of painkiller: 0.4a + 0.2b = 215

Isolate a in the first equation:
a = 750 - b

Plug into second equation and solve for b:
0.4(750 - b) + 0.2b = 215
300 - 0.4b + 0.2b = 215
85 = 0.2b
425 = b

So there are 425mls of medication B, or answer choice D.

We could also approach this as a weighted average problem. 215 mls of painkiller is 28.6666% of the 750mls of medication received. This is between 20% concentration (medication B) and 40% concentration (medication A), but slightly closer to 20% concentration. This means that there should be slightly more of medication B (20%) than medication A (40%). Half of 750 is 375, so we want our volume of B to be somewhat larger than that. This rules out all answer options but D and E. From there, we can plug in our remaining answers to see which one gets us the correct volume of painkiller.

swerve wrote:A patient is given exactly 750 millimeters of a mixture of two medications daily. Medication A contains 40% painkiller and medication B contains 20% painkiller. If the patient receives exactly 215 millimeters of painkiller daily, how many millimeters of medication B are in the mixture?

A. 150
B. 225
C. 325
D. 425
E. 550

We can let a = the amount of medication A and b = the amount of medication B and create the equations:

a + b = 750

a = 750 - b

and

0.4a + 0.2b = 215

4a + 2b = 2150

2a + b = 1,075

Substituting, we have:

2(750 - b) + b = 1075

1500 - 2b + b = 1075

1500 - b = 1075

425 = b

Answer: D