Box J and Box K are identical. ³₄ of Box J and ³₇ of Box K are filled with sand. The mass of Box K with its contents is ⁷₁₀ the mass of Box J with its contents. The total mass of the two boxes with their contents is 255 kg. Find the mass of an empty box.
Mass of Box J and its contents = 10 u
Mass of Box K and its contents = 7 u

Total mass of the two boxes with their contents
= 10 u + 7 u
= 17 u

17 u = 255 

1 u = 255 ÷ 17 = 15

Mass of Box J with its concents more than mass of Box K with its contents
= 10 u - 7 u
= 3 u
= 3 x 15
= 45 kg

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

⁹₂₈ of the capacity of sand in a box → 45
¹₂₈ of the capacity of sand in a box → 45 ÷ 9 = 5
¹²₂₈ of the capacity of sand in a box → 12 x 5 = 60 

Mass of the sand and Box K
= 7 u
= 7 x 15
= 105 kg

Mass of the empty box
= 105 - 60
= 45 kg

Answer(s): 45 kg