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Italian dressing

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by sanju09 » Fri May 14, 2010 1:40 am
A chef is using a mixture of two brands of Italian dressing. The first brand contains 10 percent vinegar, and the second brand contains 15 percent vinegar. The chef wants to make 260 milliliters of a dressing that is 13 percent vinegar. How many milliliters of 15 percent vinegar should she use?
(A) 104
(B) 116
(C) 156
(D) 184
(E) 208
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by tpr-becky » Fri May 14, 2010 8:08 am
There is an algebraic formula in which .10x+.15y=.13(260) and you can go about solving this but, becuase this algebra may be difficult for some levels you can use your answers to help you with this question.

You know that x+y=260 and that .1x + .15y=.13(260) which means .1x+.15y=33.80

When you use the answers you start at C so that you can eliminate three answers when you discover whether it works or not.

so if you use 156 for y then we know that x is equal to 104. if we take 10% of 104 we get 10.4 (by moving the decimal) if we take 15% of 156 we get 23.4 - and if you add those together you get 33.8 - which is the correct answer so C works.
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by gmatmachoman » Fri May 14, 2010 8:28 am
using the Rule of Alligation which states that

Quantity of Cheaper/Quantity of Dearer = ( Cd -Cm)/(Cm-Cc)

where Cd : Cost of Dearer Quantity
Cm : Cost of Mixture
Cc: Cost of Cheaper Quantity

Qc/Qd= (15-13)/(13-10)
=2/3

Qd/(Qc+Qd) =3/5

In 260 milliltres, we have 3/5 *260 =156ml of 15% of Vinegar!
Pick C
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by analyst218 » Fri May 14, 2010 8:38 am
sanju09 wrote:A chef is using a mixture of two brands of Italian dressing. The first brand contains 10 percent vinegar, and the second brand contains 15 percent vinegar. The chef wants to make 260 milliliters of a dressing that is 13 percent vinegar. How many milliliters of 15 percent vinegar should she use?
(A) 104
(B) 116
(C) 156
(D) 184
(E) 208
ratio of 10% to ratio of 15% = 2/3
you can get this quickly by [13-15] / [13-10]
here by [ ] i mean absolute value.
then just simple algebra 3/5 * 260=156
this method of getting ratio willsave you a huge chunck of time..
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by gmatmachoman » Fri May 14, 2010 11:58 am
analyst218 wrote:
sanju09 wrote:A chef is using a mixture of two brands of Italian dressing. The first brand contains 10 percent vinegar, and the second brand contains 15 percent vinegar. The chef wants to make 260 milliliters of a dressing that is 13 percent vinegar. How many milliliters of 15 percent vinegar should she use?
(A) 104
(B) 116
(C) 156
(D) 184
(E) 208
ratio of 10% to ratio of 15% = 2/3
you can get this quickly by [13-15] / [13-10]
here by [ ] i mean absolute value.
then just simple algebra 3/5 * 260=156
this method of getting ratio willsave you a huge chunck of time..
Yeah Agreed!! That's a basic trick when u deal with Mixtures!!
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by gmatjedi » Fri May 14, 2010 2:13 pm
0.15x + (260-x)0.1=260(0.13)
x=156
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