A patient is given exactly 750 milliliters of a mixture of two medicat

Question

A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture?

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

equation1: A+B=750 ml
equation2: .4A+.2B=215 ml
multiplying e2 by 2.5,
A+.5B=537.5 ml
subtracting from equation1,
.5B=212.5 ml
B=425 ml
D

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

BrentGMATPrepNow · Accepted Answer

Medication A: 40% pain killer Medication B: 20% pain killer We combine medications to get TOTAL of 750 ml that's approximately 29% pain killer (215/750 ≈ 29%) Important, if we combine EQUAL AMOUNTS of medications A and B (i.e., 375 mls of each), the TOTAL mixture is 30%. Since the ACTUAL mixture is 29% , we know that this mixture has MORE of medication B (20%) than medication A (40%) However, since 29% is very close to 30%, we know that a BIT MORE than half the mixture is medication B. Check the answer choices to see that D (425) is a bit more than half. Answer: D For more on this concept, please see our free video on weighted averages - https://www.gmatprepnow.com/module/gmat- ... /video/805 Cheers, Brent

Skywalker18 · Answer

Let there be A milliliters of Medication A 
and B milliliters of Medication B

A+B = 750 -- 1

Medication A contains 40% pain killer and medication B contains 20% pain killer.

(40/100)*A + (20/100)*B = 215
=> (2/5)*A + (1/5)*B = 215
Multiplying by 5 , we get

2A + B = 1075 -- 2

Equation 2- Equation 1 , we get 
A = 325 
B = 425

Answer D

chetan2u · Answer

You can convert 215 as a % of 750 or convert 40% and 20% as values.  
Always choose what saves your time. 
40% of 750 is 300, so 20% is 150.

Weighted average method is best suited now.

………………A……………Avg……….….B
…………….300…….….215………...150

\frac{B}{Total}=\frac{300-215}{300-150}=\frac{85}{150}

Quantity of B in 750 mixture =  750*\frac{85}{150}=5*85=425

D

DJ1986 · Answer

I tried algebra first but messed up and didn't get an answer choice so then I used this method but I'm not sure if it's the quickest. I probably took 3 minutes because of my mess up.

If mixture was all A it would be (2/5)750= 300 
If it was all B the mixture would be (1/5)(750) = 150

A----------given--------B
300--------215-------150
-----85----------65-----

85+65=150
so B is (85/150)(750) = 85*5 = 425

My algebra looked like this. Could someone tell me where I went wrong?

A+B = 750
(2/5)A+(1/5)B=215

(2/5)(750-B)+(1/5)B = 215
300-(2/5)B + (1/5)B = 215
(-1/5)B = -115
B=575  WRONG!!!!!!! Please Help

Skywalker18 · Answer

Hi DJ1986 , 300-(2/5)B + (1/5)B = 215 => -(1/5)B = 215 - 300 = -85 =>B = 425 Hope this helps !!

Mo2men · Answer

Hi Brent,
Really nice logic solution. However, I think there is type error. Please review the highlighted part. it should be Medicine B (20%) and A (40%)

BrentGMATPrepNow · Answer

Good catch, Mo2men!
I have edited my response.

Cheers,
Brent

anuradhaarjun · Answer

Total mixture = 750 mL
Milliliters of medication B in the mixture = B
Milliliters of medication A in the mixture = (750 - B)

Medication A contains 40% pain killer, B contains 20% pain killer, and the patient receives 215 mL.

0.4 (750 - B) + 0.2 (B) = 215
300 - 0.4*B + 0.2*B = 215
0.2*B = 85
B = 425

Answer D

gracie · Answer

A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture?

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

equation1: A+B=750 ml
equation2: .4A+.2B=215 ml
multiplying e2 by 2.5,
A+.5B=537.5 ml
subtracting from equation1,
.5B=212.5 ml
B=425 ml
D

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

equation1: A+B=750 ml
equation2: .4A+.2B=215 ml
multiplying e2 by 2.5,
A+.5B=537.5 ml
subtracting from equation1,
.5B=212.5 ml
B=425 ml
D

mm229966 · Answer

40%A + 20%B = 215
2/5 + 1/5B = 215
2A + B = 215

and if A + B = 750; then A = 325 & B = 425

Niveditha28 · Answer

Hi  chetan2u  ,  Bunuel  , i worked with percentages 
………………A……………Avg……….….B
…………….40…….….86/3………...20

I got 17:13 as the ratio . 
30x=750 
x=25

13x= 25*13=325. How is the answer 425 . The question is asking ml of medication B.

chetan2u · Answer

You have taken the ratios opposite. The quantity is more of the solution that has average closer.  More quantity pulls the average closer to itself. 
Here, 86/3 is closer to 20, so ratio of B will be more =>  \frac{B}{A}=\frac{40-28.7}{28.7-20}=\frac{11.3}{8.7}=\frac{17}{13}

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A patient is given exactly 750 milliliters of a mixture of two medicat

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