Answer:
There are 9 dimes and 15 nickels.
Step-by-step explanation:
Let number of dimes be 'd' and number of nickels be 'n'.
Given:
Total amount Debi has = $1.65
Number of nickels is 6 more than dimes.
We know that,
1 dime = $0.10
∴ 'd' dimes = $[tex]0.10d[/tex]
1 nickel = $0.05
∴ 'n' nickels = $[tex]0.05n[/tex]
As per question,
Number of nickels = 6 + number of dimes
∴ [tex]n=6+d[/tex]--------1
Also, total amount = $1.65
∴ [tex]0.10d+0.05n=1.65[/tex]------2
Now, solving equations (1) and (2) for 'n' and 'd'.
Plug in the value of 'n' from equation (1) in equation (2). This gives,
[tex]0.10d+0.05(6+d)=1.65\\0.10d+0.30+0.05d=1.65\\0.10d+0.05d=1.65-0.30\\0.15d=1.35\\d=\frac{1.35}{0.15}=9[/tex]
Therefore, the number of dimes are 9.
Number of nickels are = 9 + 6 = 15
