Question

A stack of nickel and dimes is worth $2.55. How do you find the number of nickels if the number of dimes is less than twice the number of nickels?

Answer 1

The number of nickels could be any odd number between 11 and 51 inclusive.

Explanation:

If `n` is the number of nickels and `d` is the number of dimes:

`n` must be odd Since `$2.55` can not be made up from an even number `xx0.05` plus any number `xx0.10`

If `d=0` then `n=51`
If `d=1` then `n=49`
if `d=2` then `n=47`
...and so on

We are told that `d < 2n` but this only places an lower limit on `n`:
`color(white)("XXX")`Since `5n+10d =255`
`color(white)("XXX")rarr n+2d=51`
`color(white)("XXX")`and since `2n > d`
`color(white)("XXX")rarr n+4n > 51`
`color(white)("XXX")rarr 5n > 51`
`color(white)("XXX")`and since `n` must be an integer
`color(white)("XXX")rarr n >= 11`