carlos has a box of coins that he uses when playing poker with friends. the box currently contains 45 coins, consisting of pennies, dimes, and quarters. The number of pennies is equal to the number of dimes, and the total value is $3.84. How many of each denomination does he can?

number of pennies = 19

number of dimes = 19

number of quarters = 45 - 2 * 19 = 45 - 38 = 7

Step-by-step explanation:

The total number of coins in the box is 45. The coins consist of pennies, dimes and quarters.

The number of pennies is equal to the number of dimes. The remaining number is the quarters. Therefore,

number of pennies = a

number of dimes = a

number of dimes = 45 - 2a

1 dime = 0.1 dollars

1 penny = 0.01 dollars

1 quarters = 0.25 dollars

Thee total cost can be expressed as follows

3.84 = a (0.01) + a (0.1) + 0.25 (45 - 2a)

3.84 = 0.01a + 0.1a + 11.25 - 0.5 a

3.84 = - 0.39 a + 11.25

3.84 - 11.25 = - 0.39 a

-7.41 = - 0.39 a

divide both sides by - 0.39

a = - 7.41/-0.39

a = 19

number of pennies = 19

number of dimes = 19

number of quarters = 45 - 2 * 19 = 45 - 38 = 7