Question 849555: Paula can have pennies,nickels,dimes and quarters in her purse. The average value of the coins in her purse is 20 cents. If she adds one more quarter to her the average value of all of the couns will be 21 cents. How many nickels does she have in her purse?
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20060)   (Show Source):
Answer by AnlytcPhil(1807)  (Show Source):
You can put this solution on YOUR website! Paula can have pennies,nickels,dimes and quarters in her purse. The average value of the coins in her purse is 20 cents. If she adds one more quarter to her the average value of all of the coins will be 21 cents. How many nickels does she have in her purse?
She has P pennies, N nickels, D dimes, and Q quarters
(P+5N+10D+25Q)/(P+N+D+Q) = 20
[P+5N+10D+25(Q+1)]/(P+N+D+Q+1) = 21
Clear each equation of fractions
P+5N+10D+25Q = 20(P+N+D+Q)
P+5N+10D+25(Q+1) = 21(P+N+D+Q+1)
Further rewriting:
P+5N+10D+25Q = 20(P+N+D+Q)
P+5N+10D+25Q+25 = 21(P+N+D+Q)+21
Subtracting the first equation from the second:
25 = 1(P+N+D+Q)+21
Subtract 21 from both sides
4 = P+N+D+Q
So she has exactly 4 coins
To average 20 cents before adding the quarter, she would have to have 80c
with 4 coins.
To average 21 cents after adding the quarter, she would have to have 105c
or $1.05 with 5 coins.
She could have $1.05 with 5 coins by having 4 quarters and 1 nickel. And
before the quarter was added, she would have had 3 quarters and 1 nickel,
or 80 cents, and that would be a solution.
BUT!!! Is that the only solution???
If she had only 3 quarters after the quarter was added, that would be
75 cents, and she would have to make the remaining 30 cents with 2 coins,
and that would only be possible with 1 quarter and 1 nickel.
But either way, she could only have 1 nickel. There are two possibilities
for the other coins but only one for the number of nickels.
Edwin
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