Steven's quarters total $4.20 more than his nickels. His quarters total $4.75 more than his dimes. The total value of the coins is $8.30. How many of each coin does he have?

he has 23 quarters, 31 nickels and 10 dimes.

Step-by-step explanation:

The worth of a quarter is 25 cents. Converting to dollars, it becomes

25/100 = $0.25

The worth of a nickel is 5 cents. Converting to dollars, it becomes

5/100 = $0.05

The worth of a dime is 10 cents. Converting to dollars, it becomes

10/100 = $0.1

Let x represent the number of quarter that he has.

Let y represent the number of nickels that he has.

Let z represent the number of dimes that he has

Steven's quarters total $4.20 more than his nickels. This means that

0.25x = 0.05y + 4.2

Dividing through by 0.05, it becomes

5x = y + 84

y = 5x - 84-- - - - - - - - - -1

His quarters total $4.75 more than his dimes. This means that

0.25x = 0.1z + 4.75

Dividing through by 0.1, it becomes

2.5x = z + 47.5

z = 2.5x - 47.5- - - - - - - - - -2

The total value of the coins is $8.30. This means that

0.25x + 0.05y + 0.1z = 8.3- - - - - - -3

Substituting equation 1 and equation 2 into equation 3, it becomes

0.25x + 0.05(5x - 84) + 0.1(2.5x - 47.5) = 8.3

0.25x + 0.25x - 4.2 + 0.25x - 4.75 = 8.3

0.75x - 8.95 = 8.3

0.75x = 8.3 + 8.95 = 17.25

x = 17.25/0.75

x = 23

Substituting x = 23 into equation 1, it becomes

y = 5 × 23 - 84

y = 31

Substituting x = 23 into equation 2, it becomes

z = 2.5 × 23 - 47.5

z = 10

were is the equation