"Dad wants one-cent, two-cent, three-cent, five-cent, and ten-cent stamps.

combinatorics/coinage/dimes

Problem

"Dad wants one-cent, two-cent, three-cent, five-cent, and ten-cent
stamps.  He said to get four each of two sorts and three each of the
others, but I've forgotten which.  He gave me exactly enough to buy
them; just these dimes."  How many stamps of each type does Dad want?
A dime is worth ten cents.  -- J.A.H. Hunter

Show solution

The easy way to solve this is to sell her three each, for
3x(1+2+3+5+10) = 63 cents.  Two more stamps must be bought, and they
must make seven cents (since 17 is too much), so the fourth stamps are
a two and a five.