There are 8 coins.
In my bag, one coin is worth $50. The rest are worth $10. The average value of all the coins in my bag is $15. How many coins are in my bag?
Let's say that there are x $10 coins in the bag. Then, the total value of these coins would be 10x.
We also know that there is one $50 coin in the bag, so the total value of all the coins in the bag is 10x + 50.
The average value of all the coins in the bag is $15, so we can set up the following equation:
(10x + 50)/(x + 1) = 15
Multiplying both sides by x+1, we get:
10x + 50 = 15(x + 1)
Expanding the right side, we get:
10x + 50 = 15x + 15
Subtracting 10x and 15 from both sides, we get:
35 = 5x
Solving for x, we get:
x = 7
So there are 7 $10 coins in the bag and 1 $50 coin, for a total of 8 coins in the bag.