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?

1 Answer
Alan P.
Feb 28, 2016

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#

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