Question

Mark has twice as many quarters as nickels and three more dimes than nickels. He has 4.20 in all. How many of each type of coin does he have?

Answer 1

Number of nickels = 6

number of dimes = 9

number of quarters =12

Explanation:

Let 'q' be the number of quarters and 'n' be the number of nickels

and 'd' be the number of dimes

twice as many quarters as nickels

`q=2n`

three more dimes than nickels.

`d=3+n`

1 nickel = 5 cents

1 dime = 10 cents

1 quarter = 25 cents

4.20 dollars = 420 cents

`5n+10d+25q=420`

replace q and d in the above equation

`5n+10(3+n)+25(2n)=420`

`5n+30+10n+50n=420`

`65n+30=420`

Subtract 30 from both sides

`65n=390`

divide both sides by 65

n=6

Number of nickels = 6

number of dimes =
`3+n=3+6=9`

number of quarters =
`2n=2(6)= 12`