Solution: Suppose we buy X cake, Y cake and cookies (100-x-y x-y).

3x+2y+0.5( 100-x-y)= 100

3x+2y+0.5 * 100-0.5x-0.5y = 100

3x+2y+50-0.5x-0.5y= 100

(3-0.5)x+(2-0.5)y= 100-50

2.5x+ 1.5y=50

5x+3y= 100

x = 5 x = 10 x = 15 x = 20 x = 25 x = 30

y = 17y = 14y = 1 1y = 8y = 5y = 2

Small = 78 small =76 small =74 small =72 small =70 small =68

One * * * six groups of schemes, one group can be selected.