Box E and Box F are identical. ³₄ of Box E and ³₇ of Box F are filled with sand. The mass of Box F with its contents is ⁷₉ the mass of Box E with its contents. The total mass of the two boxes with their contents is 288 kg. Find the mass of an empty box.
Mass of Box E and its contents = 9 u
Mass of Box F and its contents = 7 u

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

16 u = 288 

1 u = 288 ÷ 16 = 18

Mass of Box E with its concents more than mass of Box F with its contents
= 9 u - 7 u
= 2 u
= 2 x 18
= 36 kg

Fraction of the sand that Box E had more than Box F
= ³₄ - ³₇
= ²¹₂₈ - ¹²₂₈
= ⁹₂₈

⁹₂₈ of the capacity of sand in a box → 36
¹₂₈ of the capacity of sand in a box → 36 ÷ 9 = 4
¹²₂₈ of the capacity of sand in a box → 12 x 4 = 48 

Mass of the sand and Box F
= 7 u
= 7 x 18
= 126 kg

Mass of the empty box
= 126 - 48
= 78 kg

Answer(s): 78 kg