You have a piggy bank containing a total of 93 coins in dimes and quarters. if the piggy bank contains $14.85, how many dimes are there in piggy bank

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

      -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

There are 56 dimes in the piggy bank.

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