SOLUTION: We had this problem in math today, and i didn't understand how to get the answer. Here is the question: "Paula can have pennies,nickels,dimes, and quarters in her purse

Question 249829: We had this problem in math today, and i didn't understand how to get the answer. Here is the question:
"Paula can have pennies,nickels,dimes, and quarters in her purse. The average of the coins in Paula's purse is 20 cents. If she adds one more quarter, the average of all the coins will be 21 cents. How many nickels does she have in her purse?"
I know that the answer is one nickel, but I don't understand how to get it. Since it doesn't tell us the total number of coins in her purse, I have no idea what the first step would even be. Please help, I would really appreciate it! (:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
"Paula can have pennies,nickels,dimes, and quarters in her purse.
The average of the coins in Paula's purse is 20 cents.
If she adds one more quarter, the average of all the coins will be 21 cents.
How many nickels does she have in her purse?"
:
notice the statement,"Paula can have pennies,nickels,dimes, and quarters in her purse."
The word "can" implies you don't necessarily, have each of these type of coins
:
Let c = no. of coins
:
= 20
Multiply by c
p + 5n + 10d + 25q = 20c
:
Add a quarter
= 21
Multiply by (c+1)
p + 5n + 10d + 25(q+1) = 21(c+1)
p + 5n + 10d + 25q + 25 = 21(c+1)
p + 5n + 10d + 25q = 21c + 21 - 25
p + 5n + 10d + 25q = 21c - 4
:
Using these two equations
p + 5n + 10d + 25q = 21c - 4
p + 5n + 10d + 25q = 20c
--------------------------Subtraction eliminates everything on the left
0 = c - 4
4 = c coins originally
:
Since the average was 20, the total value would be 4 * 20 = 80
then
When you add a quarter, the total value would be 5 * 21 = 105
:
Using 4 coins how can you get 80 cents? Only one way:
3 quarters and a nickel (no pennies or dimes)
:
Add a quarter (5 coins) 4 quarters and a nickel which is 105 cents
Check
80/4 = 20 cents
105/5 = 21 cents
:
Answer is 1 nickel as you said
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