Apiggy bank contains a total of 84 coins in nickels and quarters worth $12.80.

Let's make a system of equations to solve for this:

n + q = 84

0.05n + 0.25q = 12.80

where n = nickels and q = quarters.

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Solve for n in the first equation by subtracting q from both sides.

n = 84 - q

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Plug n into the second equation.

0.05(84 - q) + 0.25q = 12.80

Distribute 0.05 inside the parentheses.

4.2 - 0.05q + 0.25q = 12.80

Combine like terms.

4.2 + 0.2q = 12.80

Subtract 4.2 from both sides.

0.2q = 8.6

Divide both sides by 0.2.

q = 43

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Plug 43 for q in the first equation.

n + (43) = 84

Subtract 43 from both sides.

n = 41

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There are 41 nickels and 43 quarters in the piggy bank. ✅