A piggy bank is full of pennies and quarters. There are 183 coins worth $12.63. How many of each coin are there?
Understand the Problem
The question is asking how many pennies and quarters are in a piggy bank, given the total number of coins and their total value. We will set up a system of equations based on the information provided to solve for the quantity of each type of coin.
Answer
There are 138 pennies and 45 quarters.
Answer for screen readers
The number of pennies is 138 and the number of quarters is 45.
Steps to Solve
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Define the Variables
Let ( p ) be the number of pennies and ( q ) be the number of quarters. -
Set Up the Equations
Based on the problem, we have two equations:
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The total number of coins: $$ p + q = 183 $$
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The total value of the coins: Since each penny is worth $0.01 and each quarter is worth $0.25, we have: $$ 0.01p + 0.25q = 12.63 $$
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Simplify the Value Equation
To eliminate decimals in the second equation, multiply through by 100: $$ p + 25q = 1263 $$ -
Substitute and Solve
Now we can solve the first equation for ( p ): $$ p = 183 - q $$
Substitute this expression for ( p ) into the simplified value equation: $$ (183 - q) + 25q = 1263 $$ -
Combine Like Terms
This simplifies to: $$ 183 + 24q = 1263 $$ -
Isolate ( q )
Subtract 183 from both sides: $$ 24q = 1080 $$
Then divide by 24: $$ q = 45 $$ -
Find ( p )
Now substitute ( q ) back to find ( p ): $$ p = 183 - 45 = 138 $$
The number of pennies is 138 and the number of quarters is 45.
More Information
In total, there are 183 coins consisting of 138 pennies and 45 quarters, which together equal $12.63.
Tips
- Not combining like terms correctly in the equations.
- Forgetting to multiply the entire equation by 100 to eliminate decimals, which can lead to incorrect values.
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