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Richard has a bank in which he saves only pennies and nickels. There are 66 coins in all. He asked his mother to count the money one day while he was at school. When he got home, she told him that he had $2.38. He asked how many of each there were but she didn't keep track. Help Richard find out how many pennies and nickels there are in his bank without him having to take them out again.

The number of coins is p + n, where p is for pennies and n is for nickels, and we know p+n = 66.

The value is 0.01p + 0.05n = 2.38.

Using the 1st equation, we know that 0.01p = 2.38 - 0.05n.

That is the same as saying p = 238 - 5n (multiply the equation by 100).

Putting p = 238 - 5n into p + n = 66 gives 238 - 5n + n = 66.

That is the same as 238 - 4n = 66.

Adding 4n to both sides and subtracting 66 from both sides gives 172 = 4n.

Dividing by 4 gives n = 43.

Since there are 66 coins, 66 - 43 = 23, and that is the number of pennies.

To check, the value of 43 nickels and 23 pennies is 43*5 + 23 cents,

and that is 2.15 + 0.23 dollars, or 2.38 dollars, which checks out.

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Algebra

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