Answer:
The data is:
Number of nickels = 246
Number of dimes = 312
Number of quarters = 204.
Now, in your group there are N people.
Dividing the coins into N people, you find that each one received the same amount of each type of coin. Then the quotient between each number of coins and N must be a whole number.
Now, you can see that the 3 numbers are even, so we know that N must be even.
For example, if N = 2, we could divide the 3 numbers of coins and get an integer in each case, but this is worded as "You and some friends" so N must be larger than 2.
Try with the next even integer:
N = 4.
nickels: 246/4 = 61.5
61.5 is not an integer: Then N can not be 4.
The next even number is N = 6.
nickels: 246/6 = 41
dimes: 312/6 = 52
quarters: 204/6 = 34
In each case we have integers, this means that 6 divides the 3 numbers of coins, so each person can receive the same amount of coins.
The we can conclude with:
There are 6 persons in the group.
Each person gets 41 nickels, 52 dimes and 34 quarters.
