Box Q and Box R are identical. ³₄ of Box Q and ³₅ of Box R are filled with sand. The mass of Box R with its contents is ⁹₁₀ the mass of Box Q with its contents. The total mass of the two boxes with their contents is 570 kg. Find the mass of an empty box.
Mass of Box Q and its contents = 10 u
Mass of Box R and its contents = 9 u

Total mass of the two boxes with their contents
= 10 u + 9 u
= 19 u

19 u = 570 

1 u = 570 ÷ 19 = 30

Mass of Box Q with its concents more than mass of Box R with its contents
= 10 u - 9 u
= 1 u
= 1 x 30
= 30 kg

Fraction of the sand that Box Q had more than Box R
= ³₄ - ³₅
= ¹⁵₂₀ - ¹²₂₀
= ³₂₀

³₂₀ of the capacity of sand in a box → 30
¹₂₀ of the capacity of sand in a box → 30 ÷ 3 = 10
¹²₂₀ of the capacity of sand in a box → 12 x 10 = 120 

Mass of the sand and Box R
= 9 u
= 9 x 30
= 270 kg

Mass of the empty box
= 270 - 120
= 150 kg

Answer(s): 150 kg