Box A and Box B are identical. ⁷₈ of Box A and ³₇ of Box B are filled with sand. The mass of Box B with its contents is ⁸₉ the mass of Box A with its contents. The total mass of the two boxes with their contents is 850 kg. Find the mass of an empty box.
Mass of Box A and its contents = 9 u
Mass of Box B and its contents = 8 u

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

17 u = 850 

1 u = 850 ÷ 17 = 50

Mass of Box A with its concents more than mass of Box B with its contents
= 9 u - 8 u
= 1 u
= 1 x 50
= 50 kg

Fraction of the sand that Box A had more than Box B
= ⁷₈ - ³₇
= ⁴⁹₅₆ - ²⁴₅₆
= ²⁵₅₆

²⁵₅₆ of the capacity of sand in a box → 50
¹₅₆ of the capacity of sand in a box → 50 ÷ 25 = 2
²⁴₅₆ of the capacity of sand in a box → 24 x 2 = 48 

Mass of the sand and Box B
= 8 u
= 8 x 50
= 400 kg

Mass of the empty box
= 400 - 48
= 352 kg

Answer(s): 352 kg