Box Q and Box R are identical. ⁶₇ of Box Q and ³₅ of Box R are filled with sand. The mass of Box R with its contents is ⁸₉ the mass of Box Q with its contents. The total mass of the two boxes with their contents is 765 kg. Find the mass of an empty box.
Mass of Box Q and its contents = 9 u
Mass of Box R and its contents = 8 u

Total mass of the two boxes with their contents
= 9 u + 8 u
= 17 u

17 u = 765 

1 u = 765 ÷ 17 = 45

Mass of Box Q with its concents more than mass of Box R with its contents
= 9 u - 8 u
= 1 u
= 1 x 45
= 45 kg

Fraction of the sand that Box Q had more than Box R
= ⁶₇ - ³₅
= ³⁰₃₅ - ²¹₃₅
= ⁹₃₅

⁹₃₅ of the capacity of sand in a box → 45
¹₃₅ of the capacity of sand in a box → 45 ÷ 9 = 5
²¹₃₅ of the capacity of sand in a box → 21 x 5 = 105 

Mass of the sand and Box R
= 8 u
= 8 x 45
= 360 kg

Mass of the empty box
= 360 - 105
= 255 kg

Answer(s): 255 kg