Question

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?

Answer 1

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23

Explanation:

Total number of coins = 43

Let number of nickels = n

Let number of dimes = d

Let number of quarters = q

`n+d+q=43 ...... (1)`

Money in n nickels =
`n * 0.05`

Money in d dimes =
`d * 0.10`

Money in q quarters =
`q * 0.25`

Total money = $7.45

`0.05n +0.10d+0.25q = 7.45\\\Rightarrow 5n +10d+25q = 745 .... (2)`

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

i.e.

`n+d=q-3`

Let us put the value in (1):

`q-3+q=43\\\Rightarrow 2q= 43+3\\\Rightarrow q =23`

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

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

`5n+10d+575 =745\\\Rightarrow 5n+10d =170\\\Rightarrow n+2d =34 .... (4)`

(4) - (3):

d = 14

Now, from (3):

n = 6

Number of nickels = 6

Number of dimes = 14

Number of quarters = 23