Box Y and Box Z are identical. ⁶₇ of Box Y and ³₈ of Box Z are filled with sand. The mass of Box Z with its contents is ⁵₈ the mass of Box Y with its contents. The total mass of the two boxes with their contents is 468 kg. Find the mass of an empty box.
Mass of Box Y and its contents = 8 u
Mass of Box Z and its contents = 5 u

Total mass of the two boxes with their contents
= 8 u + 5 u
= 13 u

13 u = 468 

1 u = 468 ÷ 13 = 36

Mass of Box Y with its concents more than mass of Box Z with its contents
= 8 u - 5 u
= 3 u
= 3 x 36
= 108 kg

Fraction of the sand that Box Y had more than Box Z
= ⁶₇ - ³₈
= ⁴⁸₅₆ - ²¹₅₆
= ²⁷₅₆

²⁷₅₆ of the capacity of sand in a box → 108
¹₅₆ of the capacity of sand in a box → 108 ÷ 27 = 4
²¹₅₆ of the capacity of sand in a box → 21 x 4 = 84 

Mass of the sand and Box Z
= 5 u
= 5 x 36
= 180 kg

Mass of the empty box
= 180 - 84
= 96 kg

Answer(s): 96 kg