SOLUTION: Alicia opens her piggy bank to find only nickles and dimes inside. She counts the coins and finds that there are 38 coins totaling $3.20. How many nickles were in the piggy bank,

Question 279801: Alicia opens her piggy bank to find only nickles and dimes inside. She counts the coins and finds that there are 38 coins totaling $3.20. How many nickles were in the piggy bank, and how many dimes where in the piggy bank?
Found 3 solutions by stanbon, solver91311, richwmiller:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Alicia opens her piggy bank to find only nickles and dimes inside.
She counts the coins and finds that there are 38 coins totaling $3.20.
How many nickles were in the piggy bank, and how many dimes where in the piggy bank?
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Equations:
Quantity: n + q = 38
Value::: 5n +25q = 320 cents
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multiply thru the Quantity equation by 4 to get:
5n + 5q = 190
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Subtract that from the Value Equation and solve for "q":
20q = 130
q = 6.5
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Note: That value of q should be a whole number.
Check the data in your problem.
==================================
Cheers,
Stan H.

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Let represent the number of nickels. Let represent the number of dimes. Each nickel is worth 5 cents, so the value of the nickels in cents is . Likewise, the value of the dimes is cents. Finally, the total amount of money is $3.20 which is the same as 320 cents. Putting it all together you have:

If you solve the first equation for in terms of you get:

giving you an expression involving that is equal to and that can be substituted in place of in the other equation.

Now solve for .

So there are 26 dimes and therefore there must be nickels.

Check: 26 dimes are worth $2.60, and 12 nickels are worth $0.60. $2.60 plus $0.60 is $3.20. Checks.

Super Double Plus Extra Credit:

Solve the system using either the Elimination Method or Cramer's Rule.

John

Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Stan read quarters when it should be dimes
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