Let the weight of the box be X pounds, and the the maximum weight you can put in the box Y pounds.

X + (2/3)Y = 130 pounds

The box and two thirds of its content weigh 130 pounds

X + (3/8)Y = 74 pounds

The box and three eights of its content weigh 74 pounds

X + (2/3)Y = 130

(2/3)Y = 130 - X (subtract X from both sides)

Y = (3/2)(130 - X) (multiply both sides by 3/2)

Now we can substitute Y in the second equation with the expression above

X + (3/8)Y = 74

X + (3/8)(3/2)(130 - X) = 74

X + 9/16(130 - X) = 74

X + 585/8 - (9/16)X = 74  (using the distributive property)

(7/16)X = 74 - 585/8 (subtract 585/8 from both sides, and subtract (9/16)X from X)

(7/16)X = 592/8 - 585/8 (74 = 592/8)

(7/16)X = 7/8

X = (7/8)*(16/7) (multiply both sides by 16/7)

X = 2 pounds

The box weighs two pounds