The fletcher family puts loose change into a jar every evening. Once a month, the family counts the coins and prepares to take it to the bank, but removes all the pennies first. Last month, they found there were 14 more quarters than dimes, and the number of nickels was 8 less than 4 times the number of dimes. If the total value of the nickels, dimes, and quarters was $15.75, how many dimes did they have?

They have 23 dimes

Step-by-step explanation:

Let x be the number of dimes

1 dime = 0.1 dollar

x dimes = 0.1x dollars

They found there were 14 more quarters than dimes.

No. of quarters = x+14

1 quarter = 0.25 dollar

(x+14) quarter = 0.25 (x+14)

The number of nickels was 8 less than 4 times the number of dimes.

So, No. of nickels = 4x-8

1 nickel = 0.05 dollar

(4x-8) nickel = 0.05 (4x-8) dollar

The total value of the nickels, dimes, and quarters was $15.75.

So, 0.1x+0.25 (x+14) + 0.05 (4x-8) = 15.75

x=23

Hence they have 23 dimes