Box R and Box S are identical. ⁴₅ of Box R and ⁵₈ of Box S are filled with sand. The mass of Box S with its contents is ⁷₈ the mass of Box R with its contents. The total mass of the two boxes with their contents is 525 kg. Find the mass of an empty box.
Mass of Box R and its contents = 8 u
Mass of Box S and its contents = 7 u

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

15 u = 525 

1 u = 525 ÷ 15 = 35

Mass of Box R with its concents more than mass of Box S with its contents
= 8 u - 7 u
= 1 u
= 1 x 35
= 35 kg

Fraction of the sand that Box R had more than Box S
= ⁴₅ - ⁵₈
= ³²₄₀ - ²⁵₄₀
= ⁷₄₀

⁷₄₀ of the capacity of sand in a box → 35
¹₄₀ of the capacity of sand in a box → 35 ÷ 7 = 5
²⁵₄₀ of the capacity of sand in a box → 25 x 5 = 125 

Mass of the sand and Box S
= 7 u
= 7 x 35
= 245 kg

Mass of the empty box
= 245 - 125
= 120 kg

Answer(s): 120 kg