Question

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

Answer 1

There are 9 dimes and 15 nickels.

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 = $
`0.10d`

1 nickel = $0.05

∴ 'n' nickels = $
`0.05n`

As per question,

Number of nickels = 6 + number of dimes

∴
`n=6+d`--------1

Also, total amount = $1.65

∴
`0.10d+0.05n=1.65`------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,

`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=(1.35)/(0.15)=9`

Therefore, the number of dimes are 9.

Number of nickels are = 9 + 6 = 15