Debi has $1.65 in a collection of dimes and nickels the number of nickels is six more than the number of dimes find the number of each type of coin

The number of dimes = 9

The number of nickels = 15

Step-by-step explanation:

The total value of all coins = $1.65

Let us assume the number of dimes = m

So, the number of nickels = Number of dimes + 6 = m + 6

Now, 1 dime = $0.1

So, m dimes = m x ($0.1) = 0.1 m

Also, 1 nickel = $0.05

So, (m + 6) nickel = (m+6) x ($0.05) = 0.05 m + 0.3

⇒ The value of m dimes + (m+6) nickels

= 0.1 m + 0.05 m + 0.3 = 0.15 m + 0.3

Also, the total value of coins is given as: $1.65

⇒ 0.15 m + 0.3 = 1.65

or, 0.15 m = 1.35

or, m = 1.35/0.15 = 9

or, m = 9

Hence, the number of dimes = 9

And the number of nickels = m + 6 = 9 + 6 = 15