Q: The price of lunch for 15 people was $207.00 including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity?
A. $11.73
B. $12.00
C. $13.80
D. $14.00
E. $15.87
So,
$207.00*85%=x ; x=price of lunch EXCLUDING gratuity
x=$175.95
avg. price per person = $175.95/15 = $11.73 (A)
Where am I going wrong? The correct answer is B
Price of Lunch
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We can plug in the answers, which represent the cost per person.The price of lunch for 15 people was $207.00,
including a 15 percent gratuity for service. What was
the average price per person, EXCLUDING the
gratuity?
(A) $11.73
(B) $12.00
(C) $13.80
(D) $14.00
(E) $15.87
Given that the total cost is an INTEGER, the correct answer is almost certainly an integer itself.
Answer choice D is too great, since 15 people paying $14 each = 15*14 = 210 -- yields a value beyond the total cost of 207.
Answer choice B: $12 per person without gratuity
Total price for 15 people = 15*12 = 180.
Price + gratuity = 180 + .15(180) = 180+27 = 207.
Success!
The correct answer is B.
Algebraic approach:
Let x = the cost per person WITHOUT gratuity.
Cost for 15 people without gratuity = 15x.
Cost for 15 people with gratuity = 115% of the cost without gratuity = (115/100)(15x).
Since the total cost with gratuity is 207, we get:
(115/100)(15x) = 207
x = (207 * 100) / (115 * 15).
Here is one way to simplify:
Divide both 100 and 15 by 5:
(207 * 100) / (115 * 15)
(207 * 20) / (115 * 3).
Divide 3 into 207; divide both 20 and 115 by 5:
(207 * 20) / (115 * 3)
(69 * 4) / 23.
Divide 23 into 69:
(69 * 4) / 23
3 * 4
12.
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Thank you!
I guess I am curious why I can't start with the total price of lunch with gratuity.
So, $207. Since this includes the 15% gratuity, then to get the price without gratuity, multiply the total price by 85% (1-gratutity (15%).
why does this not give the same answer?
I guess I am curious why I can't start with the total price of lunch with gratuity.
So, $207. Since this includes the 15% gratuity, then to get the price without gratuity, multiply the total price by 85% (1-gratutity (15%).
why does this not give the same answer?
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The step in red is the equivalent of subtracting 15% OF THE FINAL PRICE.chgordon wrote:Thank you!
I guess I am curious why I can't start with the total price of lunch with gratuity.
So, $207. Since this includes the 15% gratuity, then to get the price without gratuity, multiply the total price by 85% (1-gratutity (15%).
why does this not give the same answer?
But the gratuity is not equal to 15% of the final price; the gratuity is equal to 15% OF THE BASE PRICE.
The two values are not the same.
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Hi confused13,
In these types of situations, we have to think about the "timeline"....
Here, we had a bill, THEN the 15% gratuity was added, then we had a total:
X + .15X = 207
1.15X = 207
This is the equation that will get us the value of X...
X = 207/1.15
At NO POINT was the idea of 85% mentioned, so that should not be in your original calculation.
GMAT assassins aren't born, they're made,
Rich
In these types of situations, we have to think about the "timeline"....
Here, we had a bill, THEN the 15% gratuity was added, then we had a total:
X + .15X = 207
1.15X = 207
This is the equation that will get us the value of X...
X = 207/1.15
At NO POINT was the idea of 85% mentioned, so that should not be in your original calculation.
GMAT assassins aren't born, they're made,
Rich