Question 898715
x = pounds of black tea

Lower bound:
43 < (40x + (50)(3))/(x + 3)
43(x + 3) < 40x + 150
43x + 129 < 40x + 150
3x < 21
x < 7


Upper bound:
(40x + 150)/(x + 3) < 46
40x + 150 < 46x + 138
-6x < -12
x > 2


The merchant can use anywhere between 3 and 6 pounds of tea, inclusive.