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The question is: When the piggy bank was opened, it yielded $5.22 in nickels and pennies. If there were 162 nickels and pennies altogether, how many of each were in the bank?

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"How many of each..." actually gives a hint about how to go about solving this. We have two things that we don't know: P, the number of pennies, and N, the number of nickels.
You are probably learning systems of equations, so I'll take that approach.
You need two equations. One will simply be the number of total coins:
N + P = 162. (They gave you this!)

Then there will be an equation about the value of the coins. I'm going to write this in cents.

The total amount of cents is 522 (given), which comes from 5 cents per nickel and 1 cent per penny. In other words,
5N + 1P = 522.
I suggest elimination. Reply if you still need help...

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Is it 32 nickles and 2 pennies? – Barny William Mar 14 '11 at 15:43
No, as DJC has remarked above. Try working with the two equations here, and be sure to show/explain your work so we can help you spot your error. – The Chaz 2.0 Mar 14 '11 at 15:45

You can either use explicit elimination as suggested, or implicitly as follows. If the bank contained $\:162\:$ pennies and $\:0\:$ nickels then the total amount would be $\:\$1.62\:$, which is $\:\$3.60\:$ short of $\:\$5.22\:.\:$ Exchanging a penny for a nickel adds $\:\$0.04\:,\:$ so we need to make $\ 3.6/0.04 = 360/4\ $ exchanges.

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What have you tried? Hint: If you have $n$ nickels and $p$ pennies, how much money do you have?

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Is it 32 nickles and 2 pennies? – Barny William Mar 14 '11 at 15:40
@Barny: No, because with 32 nickels and 2 pennies, you only have 34 coins! You need them to add up to 162. – The Chaz 2.0 Mar 14 '11 at 15:43
@Barny. No, but you're on the right track. There would be $32$ nickles and $2$ pennies if the total dollar amount was $\$1.62$ and there were $34$ coins. However, your total amount is $\$5.22$, and you have $162$ coins. – JavaMan Mar 14 '11 at 15:43

90 nickels and 72 pennies =162 coins and $5.22

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perhaps a bit about how you got the answer might be helpful. – robjohn Mar 20 '13 at 16:17

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