Arithmetic Mean(3)

Let X be the Sum of the money raised by members of french club and N be the number of members.

X / N = 85

X = 85N

X - 85N = 0 ... (1)

When Jean joined, average lowered to 80. He raised 50$,

X + 50 = 80 * (N+1)

X + 50 = 80N + 80

X - 80N = 30 ... (2)

Solving (1) and (2),

5N = 30

[spoiler]N = 6[/spoiler]

IMO6. What's the OA ?

What's the OA ?

tsmith93 wrote:The members of the French Club conducted a fund-raising drive. The average (arithmetic mean) amount of money raised per member was $85. Then Jean joined the club and raised $50. This lovered the average to $80. How many members were there before Jean joined?

Before :

The group had 85 as the avg. You can view it as n 85s i.e. 85,85,85,........n terms

After Jean joined:

the avg became 80 i.e. 80,80,80...........(n+1)terms

Even Jean is considered to have raised 80 i.e additional $30. Where did this extra amount come from.

From rest of the members. In other words, rest of the members contributed $5 each to make that extra $30.

So, how many times 5 is 30 ?

tsmith93 wrote:The members of the French Club conducted a fund-raising drive. The average (arithmetic mean) amount of money raised per member was $85. Then Jean joined the club and raised $50. This lovered the average to $80. How many members were there before Jean joined?

There were x members before Jean joined, and those x must have raised $85 x already, Jean, the (x + 1)th member, raised $50 to make us write the following equation in x:

(85 x + 50) / (x + 1) = 80; solve and have

[spoiler]x = 6[/spoiler]

how do u guys come up with the solutions so fast? Is is because you have miss these one too?