Problem Solving

The price for lunch for 15 people is $207, including 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

a. $11.73
b. $12
c. $13.80
d. $14
e. $15.87

This is how I am solving this question

Finding 15% of 207

15/100 x 207 = $31.05

207 - 31.05 = $175.95 <= price for 15 people without gratuity

price per person = 175.95/15 = 11.73 (this is option A)

but the OG says that correct answer is $12, if there were no option for $11.73 then i can understand that its $12 by rounding it off.

the method that the OG uses brings the result to be $12, but my method is not wrong too, the result should be the same no matter what method you apply

someone help please

sanaa.rizwan wrote:The price for lunch for 15 people is $207, including 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

a. $11.73
b. $12
c. $13.80
d. $14
e. $15.87

This is how I am solving this question

Finding 15% of 207

15/100 x 207 = $31.05

207 - 31.05 = $175.95 <= price for 15 people without gratuity

price per person = 175.95/15 = 11.73 (this is option A)

but the OG says that correct answer is $12, if there were no option for $11.73 then i can understand that its $12 by rounding it off.

the method that the OG uses brings the result to be $12, but my method is not wrong too, the result should be the same no matter what method you apply

someone help please

Yes, 12 is correct answer.

There are 15 people and let's suppose it cost $x for each.
It costed them 207 including Tips

=> X * 15 + 15/100 (x * 15) = 207
=> x * 15( 1+3/20) = 207
=> x = 12

Since we are excluding Tips it is just 12 $ per person.

FLUID wrote:

sanaa.rizwan wrote:The price for lunch for 15 people is $207, including 15% gratuity for service. What was the average price per person, EXCLUDING the gratuity?

a. $11.73
b. $12
c. $13.80
d. $14
e. $15.87

This is how I am solving this question

Finding 15% of 207

15/100 x 207 = $31.05

207 - 31.05 = $175.95 <= price for 15 people without gratuity

price per person = 175.95/15 = 11.73 (this is option A)

but the OG says that correct answer is $12, if there were no option for $11.73 then i can understand that its $12 by rounding it off.

the method that the OG uses brings the result to be $12, but my method is not wrong too, the result should be the same no matter what method you apply

someone help please

Yes, 12 is correct answer.

There are 15 people and let's suppose it cost $x for each.
It costed them 207 including Tips

=> X * 15 + 15/100 (x * 15) = 207
=> x * 15( 1+3/20) = 207
=> x = 12

Since we are excluding Tips it is just 12 $ per person.

Yes. 12 is the correct answer. Sanaa, in your approach you are reducing 15% of the total bill i.e. $207
where as according to the question the 15% gratuity is on the per head cost and not on the total bill.
hence the correct approach is as shown by FLUID.

Hope this helps.

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 -- 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.

I have the same question and I don't really get it, why can't we just 207*0,85 instead of 207/1,15 when we are looking for 15%? Shouldn't it be the same?

=

shurale wrote:I have the same question and I don't really get it, why can't we just 207*0,85 instead of 207/1,15 when we are looking for 15%? Shouldn't it be the same?

X is 15% greater than Y does NOT imply that Y is 15% less than X or that Y is 85% of X.

In the problem above, let P = the final price with gratuity and C = the total cost for 15 people without gratuity.

Since the final price is 15% greater than the cost without gratuity, we get:
P = (115/100)C
P = (23/20)C
C = (20/23)P.

Thus, the cost without gratuity is equal to 20/23 -- not 85% -- of the final price with gratuity.

Since P = 207, we get:
C = (20/23)(207) = 180.
Since there are 15 people, the cost per person without gratuity = 180/15 = 12.

One more way.

x + 15x/100 = 207
115x = 20700
x = 12

dears

try to understand the approach for such question


putting 15% for 207 is wrong it's 15% of X + X = 207

so calculate in such manner that 207/1.15 = actual value

now divide actual value by 15

= 12