Box D and Box E are identical. ³₄ of Box D and ²₇ of Box E are filled with sand. The mass of Box E with its contents is ⁷₉ the mass of Box D with its contents. The total mass of the two boxes with their contents is 624 kg. Find the mass of an empty box.
Mass of Box D and its contents = 9 u
Mass of Box E and its contents = 7 u

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

16 u = 624 

1 u = 624 ÷ 16 = 39

Mass of Box D with its concents more than mass of Box E with its contents
= 9 u - 7 u
= 2 u
= 2 x 39
= 78 kg

Fraction of the sand that Box D had more than Box E
= ³₄ - ²₇
= ²¹₂₈ - ⁸₂₈
= ¹³₂₈

¹³₂₈ of the capacity of sand in a box → 78
¹₂₈ of the capacity of sand in a box → 78 ÷ 13 = 6
⁸₂₈ of the capacity of sand in a box → 8 x 6 = 48 

Mass of the sand and Box E
= 7 u
= 7 x 39
= 273 kg

Mass of the empty box
= 273 - 48
= 225 kg

Answer(s): 225 kg