Problem Solving

Nine persons went to a hotel for taking their meals. Eight of them spent 12$ each on their meals and the ninth spent 8$ more than the average expenditure of all the nine. What was the total money spent by them.

A)115$
B)116$
C)117$
D)118$
E)119$

OA: [spoiler]C[/spoiler]

coolhabhi wrote:Nine persons went to a hotel for taking their meals. Eight of them spent 12$ each on their meals and the ninth spent 8$ more than the average expenditure of all the nine. What was the total money spent by them.

A)115$
B)116$
C)117$
D)118$
E)119$

We can PLUG IN THE ANSWERS, which represent the total spent.
Since there are 9 people, the correct answer is probably a MULTIPLE OF 9.
For an integer to be a multiple of 9, the sum of its digits must be a multiple of 9.
Only C -- 1+1+7 = 9 -- satisfies this constraint.
When the correct answer choice is plugged in, the first 8 people will spend $12 each.

Answer choice C: 117
Average price per person = 117/9 = 13.
Since the 9th person spent $8 more than the average, price for the 9th person = 13+8 = 21.
Thus, the total for the first 8 people = 117-21 = 96.
Price for each of the first 8 people = 96/8 = 12.
Success!

The correct answer is C.

How about one more? This seems pretty intuitive:

Let's suppose the average is x.

The total amount spent is 9x, since we have (nine people) * (an average of x).

But the total amount spent is also 8*12 + x + 8. ($12 by the first 8, and (x + 8) by the last guy.)

So we have 9x = 8*12 + x + 8, which reduces to x = 13. Thus the total spent is 9*13, or 117.