"A merchant has 3 items on sale: namely, a radio for $50, a clock for $30, and a flashlight for $1. At the end of the day, she has sold a total of 100 of the 3 items and has taken exactly $1000 on the total sales. How many radios did he sell?"
This is not a particularly simple problem, as it is over-defined. It turns out to be a test of integer programming. However, this does not mean it should be approached initially any different than any other problem.
Step #1 - Name Stuff.
R = # of radios sold
C = # of clocks sold
F = # of flashlights sold
R + C + F = 100
50*R + 30*C + 1*F = 1000
The most logical substitution would be F = 100 - R - C, giving
50*R + 30*C + (100 - R - C) = 1000
49*R + 29*C = 900
If this were a continuous problem, there would be infinitely many solutions. It's not a continuous problem. Radios and Clocks don't sell in half-units.
One thing that will help is noticing that (900 - 49*R)/29 must be an integer.
Good luck. Let's see what you get.