A country singer made 2,000 for his last show. He enjoys boots and hats. Each pair of boots costs 100 and each hat costs 50. What is the best...

Hello!

As I understand, a singer is going to spend all that 2000 for boots and hats. If we denote the number of boots pairs as b and the number of hats as h, then we obtain a linear inequality

100b + 50h <= 2000, or 2b + h <= 40.

Also of course 0 <= b <= 2000/100 = 20 and 0 <= h <= 2000/50 = 40. These inequalities describe the triangle with the vertices (0, 0), (20, 0) and (0, 40) on the (b, h) plane.

Unfortunately, you didn't give any additional  conditions to choose what combination is better for a singer. If he wants a maximum number of kits (a hat + a pair of boots), then he can buy a maximum of 13 kits and 50($) remains so he can by one more hat.