A box contains $7.45 in nickels, dimes, and quarters. There are 43 coins in all, and the sum of the numbers of nickels and dimes is 3 less than the number of quarters. How many coins of each kind are there?

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23

Step-by-step explanation:

Total number of coins = 43

Let number of nickels = n

Let number of dimes = d

Let number of quarters = q

Money in n nickels =

Money in d dimes =

Money in q quarters =

Total money = $7.45

The sum of the numbers of nickels and dimes is 3 less than the number of quarters.

i.e.

Let us put the value  in (1):

Putting the value of q in (1) and (2):

n+d = 20 .... (3)

(4) - (3):

d = 14

Now, from (3):

n = 6

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23