Adam will use x black stone tiles and y gray stone tiles to cover his patio floor. Black stone tiles cost $5 each and gray stone tiles cost $4 each. He can spend up to $150 on his project, and he wants the number of gray stone tiles to be less than half the number of black stone tiles.

As given, Let the number of black tiles be represented by = xLet the number of gray tiles be represented by = yAs the cost of one black tile is $5 and one gray tile is $4 and Adam can spend only up to $150, inequality becomes, [tex]5x+4y\leq 150[/tex]Also, he wants the number of gray stone tiles to be less than half the number of black stone tiles, so equation becomes, [tex]y<\frac{x}{2}[/tex]