Box W and Box X are identical. ⁷₈ of Box W and ³₇ of Box X are filled with sand. The mass of Box X with its contents is ⁵₈ the mass of Box W with its contents. The total mass of the two boxes with their contents is 650 kg. Find the mass of an empty box.
Mass of Box W and its contents = 8 u
Mass of Box X and its contents = 5 u

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

13 u = 650 

1 u = 650 ÷ 13 = 50

Mass of Box W with its concents more than mass of Box X with its contents
= 8 u - 5 u
= 3 u
= 3 x 50
= 150 kg

Fraction of the sand that Box W had more than Box X
= ⁷₈ - ³₇
= ⁴⁹₅₆ - ²⁴₅₆
= ²⁵₅₆

²⁵₅₆ of the capacity of sand in a box → 150
¹₅₆ of the capacity of sand in a box → 150 ÷ 25 = 6
²⁴₅₆ of the capacity of sand in a box → 24 x 6 = 144 

Mass of the sand and Box X
= 5 u
= 5 x 50
= 250 kg

Mass of the empty box
= 250 - 144
= 106 kg

Answer(s): 106 kg