umasarath52 wrote: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
We can plug in the answers, which represent the cost per person.
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.
15% of 207 is 31.05, and the total amount WITHOUT gratuity is 207-31.05 = 175.95
and the individual price per person is 175.95/15 = 11.73
Please explain what is wrong with the above method.
The step in red implies that the gratuity is equal to 15% OF THE FINAL PRICE ($207).
Not so.
The gratuity is equal to 15% OF THE BASE PRICE ($180, as shown in my solution above).
Also:
ALWAYS VERIFY THAT YOUR ANSWER CHOICE MAKES SENSE.
If the base price per person = $11.73, then the gratuity per person = 15% of 11.73 = $1.7595.
A gratuity that includes $.0095 is not viable.
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