SOLUTION: A purse contains a collection of quarters, dimes, nickels, and pennies. The average value of the coins in the purse is 17 cents. If a penny is removed from the purse, the average v

Click here to see ALL problems on Miscellaneous Word Problems

Question 285547: A purse contains a collection of quarters, dimes, nickels, and pennies. The average value of the coins in the purse is 17 cents. If a penny is removed from the purse, the average value of the coins becomes 18 cents. How many nickels are in the purse?
(A) 2 (B) 5 (C) 0 (D) 1 (E) 8
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The average value would be
(total value)/(number of coins)
Let = number of quarters
Let = number of dimes
Let = number of nickels
Let = number of pennies
given:
(1) (in cents)
(1)
and

(2)
Comparing (1) and (2) I can say

Subtract from both sides

Going back to (1),
(1)
(1)
(in cents)
There must be coins, making cents
I know there must be at least pennies
and there could be or pennies
There can't be quarters, since that adds to cents
There can't be quarters either, since dime and
nickel make -too much
Suppose there are quarters, dime, nickel,
and pennies
That makes , but coins
and I can't make up cents with more coin
I'm guessing there are quarters -you can figure out the rest