Answer:
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
[tex]n+d+q=43 ...... (1)[/tex]
Money in n nickels = [tex]n \times 0.05[/tex]
Money in d dimes = [tex]d \times 0.10[/tex]
Money in q quarters = [tex]q \times 0.25[/tex]
Total money = $7.45
[tex]0.05n +0.10d+0.25q = 7.45\\\Rightarrow 5n +10d+25q = 745 .... (2)[/tex]
The sum of the numbers of nickels and dimes is 3 less than the number of quarters.
i.e.
[tex]n+d=q-3[/tex]
Let us put the value in (1):
[tex]q-3+q=43\\\Rightarrow 2q= 43+3\\\Rightarrow q =23[/tex]
Putting the value of q in (1) and (2):
n+d = 20 .... (3)
[tex]5n+10d+575 =745\\\Rightarrow 5n+10d =170\\\Rightarrow n+2d =34 .... (4)[/tex]
(4) - (3):
d = 14
Now, from (3):
n = 6
Number of nickels = 6
Number of dimes = 14
Number of quarters = 23
