Zachary has nickels, dimes and quarters in his piggy bank. He has 58 coins with a total value of $6.50. There are twice as many dimes as nickel. How many of each coin does he have?

nickel = 16

dimes = 32

quarters = 10

Step-by-step explanation:

Given that,

number of coins Zachery have in his piggy bank = 58

total money Zachery have in his piggy bank = $6.50

Suppose number of nickel = x

number of dimes = 2x

number of quarters = y

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Equation 1

x + 2x + y = 58

3x + y = 58

Equation 2

x (0.05) + 2x (0.10) + y (0.25) = 6.50

0.05x + 0.2x + 0.25y = 6.50

0.25x + 0.25y = 6.50

y = 58 - 3x

put value of y in equation 2

0.25x + 0.25 (58 - 3x) = 6.50

0.25x + 14.5 - 0.75x = 6.50

-0.5x = 6.50 - 14.5

-0.5x = - 8

x = 16

y = 58 - 3x

y = 58 - 3 (16)

y = 10

number of nickel = x = 16

number of dimes = 2x = 32

number of quarters = y = 10