Box V and Box W are identical. ⁴₅ of Box V and ²₇ of Box W are filled with sand. The mass of Box W with its contents is ⁷₈ the mass of Box V with its contents. The total mass of the two boxes with their contents is 270 kg. Find the mass of an empty box.
Mass of Box V and its contents = 8 u
Mass of Box W and its contents = 7 u

Total mass of the two boxes with their contents
= 8 u + 7 u
= 15 u

15 u = 270 

1 u = 270 ÷ 15 = 18

Mass of Box V with its concents more than mass of Box W with its contents
= 8 u - 7 u
= 1 u
= 1 x 18
= 18 kg

Fraction of the sand that Box V had more than Box W
= ⁴₅ - ²₇
= ²⁸₃₅ - ¹⁰₃₅
= ¹⁸₃₅

¹⁸₃₅ of the capacity of sand in a box → 18
¹₃₅ of the capacity of sand in a box → 18 ÷ 18 = 1
¹⁰₃₅ of the capacity of sand in a box → 10 x 1 = 10 

Mass of the sand and Box W
= 7 u
= 7 x 18
= 126 kg

Mass of the empty box
= 126 - 10
= 116 kg

Answer(s): 116 kg