Box P and Box Q are identical. ⁴₅ of Box P and ²₇ of Box Q are filled with sand. The mass of Box Q with its contents is ⁷₉ the mass of Box P with its contents. The total mass of the two boxes with their contents is 720 kg. Find the mass of an empty box.
Mass of Box P and its contents = 9 u
Mass of Box Q and its contents = 7 u

Total mass of the two boxes with their contents
= 9 u + 7 u
= 16 u

16 u = 720 

1 u = 720 ÷ 16 = 45

Mass of Box P with its concents more than mass of Box Q with its contents
= 9 u - 7 u
= 2 u
= 2 x 45
= 90 kg

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

¹⁸₃₅ of the capacity of sand in a box → 90
¹₃₅ of the capacity of sand in a box → 90 ÷ 18 = 5
¹⁰₃₅ of the capacity of sand in a box → 10 x 5 = 50 

Mass of the sand and Box Q
= 7 u
= 7 x 45
= 315 kg

Mass of the empty box
= 315 - 50
= 265 kg

Answer(s): 265 kg