Box E and Box F are identical. ³₄ of Box E and ³₅ of Box F are filled with sand. The mass of Box F with its contents is ⁷₈ the mass of Box E with its contents. The total mass of the two boxes with their contents is 495 kg. Find the mass of an empty box.
Mass of Box E and its contents = 8 u
Mass of Box F and its contents = 7 u

Total mass of the two boxes with their contents
= 8 u + 7 u
= 15 u

15 u = 495 

1 u = 495 ÷ 15 = 33

Mass of Box E with its concents more than mass of Box F with its contents
= 8 u - 7 u
= 1 u
= 1 x 33
= 33 kg

Fraction of the sand that Box E had more than Box F
= ³₄ - ³₅
= ¹⁵₂₀ - ¹²₂₀
= ³₂₀

³₂₀ of the capacity of sand in a box → 33
¹₂₀ of the capacity of sand in a box → 33 ÷ 3 = 11
¹²₂₀ of the capacity of sand in a box → 12 x 11 = 132 

Mass of the sand and Box F
= 7 u
= 7 x 33
= 231 kg

Mass of the empty box
= 231 - 132
= 99 kg

Answer(s): 99 kg