Question

A man has two more nickels than dimes. He has $1.15 in all. How many coins of each kind does he have?

Answer 1

Man has 9 Nickels and 7 dimes.

Explanation:

Let Number of dimes be x

and Number of Nickels be y

As Per given data he has two more nickels than dimes.

`y= 2+x\\`

As we know that

1
`\$` = 100 cent

1 nickel is worth = 5 cents =
`(5)/(100)`= 0.05
`\$`

1 dime is worth = 10 cents =
`(10)/(100)` 0 .1
`\ $`

According to given data he has
`\$\ 1.15` total nickel and dimes

So the equation becomes,

`0.05y+0.1x=1.15`

but
`y= 2+x`

`0.05(2+x)+0.1x=1.15\\0.1+0.05x+0.1x=1.15\\0.1+0.15x= 1.15\\0.15x= 1.15-0.1\\0.15x=1.05\\x=(1.05)/(0.15)= 7`

Substituting value of x in equation
`y = 2+x` we get

`y= 2+7 =9`

Man has 9 Nickels and 7 dimes.