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

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29 Oct 2015, 09:41

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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

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, 18:17

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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 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

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

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20 Feb 2016, 07:14

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 Answer B.

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

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20 Feb 2016, 08:22

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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

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

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19 Nov 2017, 04:47

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