Let d = number of dimes.
Let q = number of quarters.
The total number of coins is 93, so the first equation is
d + q = 93
The value of 1 dime is $0.10. The value of 1 quarter is $0.25.
d dimes are worth 0.1d, and q quarters are worth 0.25q.
The total value of the coins is $14.85, so that gives us our second equation.
0.1d + 0.25q = 14.85
Now we have a system of two equations in two unknowns.
d + q = 93
0.1d + 0.25q = 14.85
Rewrite the first equation. Then multiply both sides of the second equation by -10, and write it underneath. Then add the equations.
d + q = 93
-d - 2.5q = -148.5
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-1.5q = -55.5
Divide both sides by -1.5.
q = 37
Now substitute 37 for q in the first original equation and solve for d.
d + q = 93
d + 37 = 93
Subtract 37 from both sides.
d = 56
Answer: There are 56 dimes in the piggy bank.
