Box L and Box M are identical. ³₄ of Box L and ²₅ of Box M are filled with sand. The mass of Box M with its contents is ⁷₈ the mass of Box L with its contents. The total mass of the two boxes with their contents is 420 kg. Find the mass of an empty box.
Mass of Box L and its contents = 8 u
Mass of Box M and its contents = 7 u

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

15 u = 420 

1 u = 420 ÷ 15 = 28

Mass of Box L with its concents more than mass of Box M with its contents
= 8 u - 7 u
= 1 u
= 1 x 28
= 28 kg

Fraction of the sand that Box L had more than Box M
= ³₄ - ²₅
= ¹⁵₂₀ - ⁸₂₀
= ⁷₂₀

⁷₂₀ of the capacity of sand in a box → 28
¹₂₀ of the capacity of sand in a box → 28 ÷ 7 = 4
⁸₂₀ of the capacity of sand in a box → 8 x 4 = 32 

Mass of the sand and Box M
= 7 u
= 7 x 28
= 196 kg

Mass of the empty box
= 196 - 32
= 164 kg

Answer(s): 164 kg