Economist GMAT
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
OA B.
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Grandmother's Punch hangover cure is a mix of two
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fskilnik@GMATH
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Excellent occasion for the alligation :AAPL wrote:Economist GMAT
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
\[? = x\,\,\,\left[ {{\text{ml}}} \right]\]
\[\frac{x}{{750}} = \frac{{20 - \frac{{58}}{5}}}{{20 - 5}}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,750} \,\,\,\,\,\,\,? = x = \frac{{750\left( {100 - 58} \right)}}{{5 \cdot 15}} = \frac{{150 \cdot 42}}{{15}} = 420\,\,\,\left[ {{\text{ml}}} \right]\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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We can PLUG IN THE ANSWERS, which represent the amount of cider.AAPL wrote:Economist GMAT
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
When the correct answer is plugged in, the amount of alcohol in the 750 ml bottle = 87 ml.
Since the alcohol percentage in the cider = 5% = 1/20, the correct answer is almost
certain to be a multiple of 20.
Of the five answer choices, only B is a multiple of 20.
B: 420 ml cider, implying that the extraction = 750-420 = 330 ml
Total alcohol = (5% of 420 ml of cider) + (20% of 330 ml of extraction) = 21 + 66 = 87,
Success!
The correct answer is B.
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As a tutor, I don't simply teach you how I would approach problems.
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Hi All,
We're told that 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. We're asked if a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contain. This question can be solved in a variety of different ways, including Algebraically:
H = number of milliliters of herbal extract
A = number of milliliters of apricot cider
With 750 total milliliters and 87 milliliters of alcohol, we can create the following equations:
H + A = 750
(.2H + .05A) = 87
We can multiply the second equation by 20...
4H + A = 1740
and then substitute in H = (750 - A) ....
4(750 - A) + A = 1740
3000 - 4A + A = 1740
1260 - 3A = 0
1260 = 3A
420 = A
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that 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. We're asked if a 750-milliliter Grandmother's Punch bottle has 87 milliliters of alcohol, how much apricot cider does it contain. This question can be solved in a variety of different ways, including Algebraically:
H = number of milliliters of herbal extract
A = number of milliliters of apricot cider
With 750 total milliliters and 87 milliliters of alcohol, we can create the following equations:
H + A = 750
(.2H + .05A) = 87
We can multiply the second equation by 20...
4H + A = 1740
and then substitute in H = (750 - A) ....
4(750 - A) + A = 1740
3000 - 4A + A = 1740
1260 - 3A = 0
1260 = 3A
420 = A
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
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Scott@TargetTestPrep
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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:AAPL wrote:Economist GMAT
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
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.
Answer: B
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