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# Grandmother's Punch hangover cure is a mix of two ingredients: a herba

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Grandmother's Punch hangover cure is a mix of two ingredients: a herba  [#permalink]

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Updated on: 29 Oct 2015, 11:26
2
8
00:00

Difficulty:

55% (hard)

Question Stats:

72% (02:54) correct 28% (03:04) wrong based on 219 sessions

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Grandmother's Punch hangover cure is a mix of two ingredients: a herbal extraction that contains 20% alcohol and apricot cider that contains 5% alcohol. If a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contains?

A. 330 milliliters
B. 420 milliliters
C. 565 milliliters
D. 630 milliliters
E. 670 milliliters

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Originally posted by shyind on 29 Oct 2015, 10:41.
Last edited by Bunuel on 29 Oct 2015, 11:26, edited 1 time in total.
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Re: Grandmother's Punch hangover cure is a mix of two ingredients: a herba  [#permalink]

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29 Oct 2015, 19:14
3
1
3
Herbal Extraction = x
Apricot Cider = y

Question asks the quantity of y.

x + y = 750 ml....................Eq 1.
0.2 x + 0.05 y = 87 ml..............Eq 2.

Two equations, two variables, on solving we get y to be 420.
##### General Discussion
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Re: Grandmother's Punch hangover cure is a mix of two ingredients:  [#permalink]

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29 Oct 2015, 11:34
let herbal extraction be denoted H and other A
case 1:
if H: 350 and A:400
20%-70 and 5%-20 --- total 90 ml

case 2:
if H:300 and A:450
20%-60 and 5%-22.5--- 82.5 ml

therefore A is between 400 and 450 ml : ans b
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Re: Grandmother's Punch hangover cure is a mix of two ingredients: a herba  [#permalink]

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29 Oct 2015, 12:00
shyind wrote:
Grandmother's Punch hangover cure is a mix of two ingredients: a herbal extraction that contains 20% alcohol and apricot cider that contains 5% alcohol. If a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contains?

A. 330 milliliters
B. 420 milliliters
C. 565 milliliters
D. 630 milliliters
E. 670 milliliters

The mixture contains 87 mL of alcohol. If the two ingredients were mixed in a 50-50 proportion, we would have 93.75 mL of alcohol ((.20 x 375) + (.05 x 375) = 75mL + 18.75 mL = 93.75). Since we have less than this, we KNOW that there should be more of the Apricot Cider mixed in than the Herbal extraction - but since 93.75 is not too much greater than 87, the mixture will not be to far from 50-50. From this initial calculation, we can get rid of A, D and E . A would create a mixture with too much alcohol and and D and E would create mixtures with too little alcohol.

Next, by looking at the answer choices remaining (B and C), we can rule out C. Just using number properties, we can see that 565 will not yield a whole number result. That is 565 x .05 will yield a decimal (ending in .25. Actually, it would be 28.25). The amount of alcohol resulting from the Herbal extraction would have be a decimal that ends in .75 for this answer choice to give us a whole number. Since the Herbal extraction is 20% alcohol, we know that it cannot - since the number of mL of the Herbal extraction is whole and will end in 5.

UUsing this same logic, 420 mL of apricot cider (at 5%) would yield a whole number - as would 330 mL of the herbal extract (at 20%). Thus, answer choice B is correct.
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Re: Grandmother's Punch hangover cure is a mix of two ingredients: a herba  [#permalink]

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29 Oct 2015, 19:17
3
shyind wrote:
Grandmother's Punch hangover cure is a mix of two ingredients: a herbal extraction that contains 20% alcohol and apricot cider that contains 5% alcohol. If a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contains?

A. 330 milliliters
B. 420 milliliters
C. 565 milliliters
D. 630 milliliters
E. 670 milliliters

I will post 2 methods for this question.

Method 1 Weighted Average Allegation Method:

Herbal Extraction---------Combined(Grandmother's Punch hangover cure)-------------Apricot Cider
__________$$\frac{1}{5}$$_________________________$$\frac{87}{750}$$_______________________________$$\frac{1}{20}$$

The absolute differences between each individual ingredient with its combined mixture are in a ratio. Let H denote Herbal Extraction weight and Let A denote Apricot Cider weight.

($$\frac{87}{750}$$-$$\frac{1}{5}$$)H = ($$\frac{1}{20}$$-$$\frac{87}{150}$$)A -------------->$$\frac{H}{A}$$=$$\frac{66}{84}$$
Apricot Cider's volume is 56% of the combined mixture ($$\frac{84}{(66+84)}*100$$)
56% of 750 = 420. Correct answer choice is B.

Method 2 System of Equations Method:

(1)H+A=750
(2).2H+.05A=87

Rewrite(1)
(1) .2H+.2A=150
(2) .2H+.05A=87

Subtract (2) from (1). The resulting equation is .15A= 63 ---> A= 420
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Re: Grandmother's Punch hangover cure is a mix of two ingredients: a herba  [#permalink]

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20 Feb 2016, 08:14
I think in this question using the formula of mix problems will handle it more quickly.
87/750 = 11,6%
(20-11,6)/(11,6-5) = 8,4/6,6 = 14/11
<=> total parts = 25
750/25 = 30
Ac = 30*14 = 420
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Re: Grandmother's Punch hangover cure is a mix of two ingredients: a herba  [#permalink]

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20 Feb 2016, 09:22
1
H= Herbal; A=Apricot
H+A = 750
1. Since alcohol is 87, hence, other stuff (Herbal and Apricot) is 750-87 = 663.
2. 20% of H is alcohol; hence, 80% is H
3. 5% of A is alcohol; hence 95% is A
.8H+.95A=663
H=750-A
.8(750-A)+.95A = 663
600-.8A+.95A = 663
.15A = 63
A=63/.15
A=420
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Re: Grandmother's Punch hangover cure is a mix of two ingredients: a herba  [#permalink]

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17 Sep 2018, 12:32
shyind wrote:
Grandmother's Punch hangover cure is a mix of two ingredients: a herbal extraction that contains 20% alcohol and apricot cider that contains 5% alcohol. If a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contains?

A. 330 milliliters
B. 420 milliliters
C. 565 milliliters
D. 630 milliliters
E. 670 milliliters

Excellent occasion for the alligation :

$$? = x\,\,\,\left[ {{\text{ml}}} \right]$$

$$\frac{x}{{750}} = \frac{{20 - \frac{{58}}{5}}}{{20 - 5}}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,750} \,\,\,\,\,\,\,? = x = \frac{{750\left( {100 - 58} \right)}}{{5 \cdot 15}} = \frac{{150 \cdot 42}}{{15}} = 420\,\,\,\left[ {{\text{ml}}} \right]$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Grandmother's Punch hangover cure is a mix of two ingredients: a herba  [#permalink]

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17 Sep 2018, 14:19
h+a=750
.2h+.05a=87

h=750-a
.2(750-a)+.05a=87
150-.2a+.05a=87
.15a=63
a=6300/15=420
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Re: Grandmother's Punch hangover cure is a mix of two ingredients: a herba  [#permalink]

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18 Sep 2018, 18:45
shyind wrote:
Grandmother's Punch hangover cure is a mix of two ingredients: a herbal extraction that contains 20% alcohol and apricot cider that contains 5% alcohol. If a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contains?

A. 330 milliliters
B. 420 milliliters
C. 565 milliliters
D. 630 milliliters
E. 670 milliliters

Let’s let H = the number of milliliters of the herbal extraction and A = the number of milliliters of the apricot cider. We can create the equations:

0.2H + 0.05A = 87

20H + 5A = 8700

4H + A = 1,740

A = 1,740 - 4H

And

A + H = 750

So H = 750 - A. Substituting 750 - A for H in A = 1,740 - 4H, we have:

A = 1,740 - 4(750 - A)

A = 1,740 - 3,000 + 4A

-3A = -1,260

A = 420

Alternate Solution:

We have x milliliters of herbal extraction that has 20% alcohol. We add (750 – x) milliliters of apricot cider that has 5% alcohol. The result is a solution of Grandma’s Punch that contains 87 milliliters of alcohol. We can express this as:

0.20x + (750 – x)(0.05) = 87

0.20 x + 37.5 – 0.05x = 87

0.15x = 49. 5

x = 330

Since we have 330 milliliters of herbal extraction, then we have (750 – 330) = 420 milliliters of apricot cider.

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Re: Grandmother's Punch hangover cure is a mix of two ingredients: a herba   [#permalink] 18 Sep 2018, 18:45
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