Question

Luis is saving money to purchase a new video game. He has a total of 30 coins consisting of nickels and dimes. The value of the coins is $2.20. Let n represent the number of nickels and let d represent the number of dimes. Which system of equations can be used to determine the number of nickels and the number of dimes Luis has?

Answer 1

n + d = 30 and 5n + 10d =220

Answer 2

`n+d=30` and

`0.05n+0.10d=2.20`

Explanation:

Let n represent the number of nickels

Let d represent the number of dimes.

Luis has a total of 30 coins; equation becomes:

`n+d=30`

or
`n=30-d` ..... (1)

The value of the coins is $2.20 ; equation becomes:

{a dime is worth 10 cents and a nickel is 5 cents}

`0.05n+0.10d=2.20` ..... (2)

Putting the value of n from (1) in (2)

`0.05(30-d)+0.10d=2.20`

=>
`1.5-0.05d+0.10d=2.20`

=>
`0.05d=2.20-1.5`

=>
`0.05d=0.7`

=> d=14

And n=30-d

so,
`n=30-14=16`

So, the system of equations used to determine the number of nickels and the number of dimes Luis has are :

`n+d=30` and

`0.05n+0.10d=2.20`