Given a number of 3in squares and 2in squares, how many of each are needed to get a total area of 35 in^2?
Through quick trial and error (the method they wanted I believe) you find that you need 3 3in squares and 2 2in squares, but I got to thinking on how to solve this exactly.
You have 2 unknowns and the following info:
4x + 9y = 35
x >= 0, y >= 0, x and y are both integers.
It also follows then that x <= 8 and y <= 3
I'm not sure how to use the inequalities or the integer only info to form a direct 2nd equation in order to solve the system of equations. How would you do this without trial and error?