SOLUTION: Paula can have pennies, nickels, dimes, and quarters in her purse. The average value of coins in her purse is 20 cents. If she adds one more quarter to her purse, the average value

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Question 246221: Paula can have pennies, nickels, dimes, and quarters in her purse. The average value of coins in her purse is 20 cents. If she adds one more quarter to her purse, the average value of all the coins will be 21 cents. How many nickels does she have in her purse?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = amount of money in her purse
Let n = number of coins in her purse
given:
a%2Fn+=+20
%28a+%2B+25%29%2F%28n+%2B+1%29+=+21
---------------------
a+=+20n
%2820n+%2B+25%29%2F%28n+%2B+1%29+=+21
20n+%2B+25+=+21%2A%28n+%2B+1%29
20n+%2B+25+=+21n+%2B+21
n+=+4
a+=+20%2A4
a+=+80
The only 4 coins that give me 80 cents is 3 quarters and 1 nickel
she has 1 nickel
check:
%2820n+%2B+25%29%2F%28n+%2B+1%29+=+21
%2820%2A4+%2B+25%29%2F5+=+21
105%2F5+=+21
105+=+105
OK