Box E and Box F are identical. ⁶₇ of Box E and ²₅ of Box F are filled with sand. The mass of Box F with its contents is ⁵₈ the mass of Box E with its contents. The total mass of the two boxes with their contents is 416 kg. Find the mass of an empty box.
Mass of Box E and its contents = 8 u
Mass of Box F and its contents = 5 u

Total mass of the two boxes with their contents
= 8 u + 5 u
= 13 u

13 u = 416 

1 u = 416 ÷ 13 = 32

Mass of Box E with its concents more than mass of Box F with its contents
= 8 u - 5 u
= 3 u
= 3 x 32
= 96 kg

Fraction of the sand that Box E had more than Box F
= ⁶₇ - ²₅
= ³⁰₃₅ - ¹⁴₃₅
= ¹⁶₃₅

¹⁶₃₅ of the capacity of sand in a box → 96
¹₃₅ of the capacity of sand in a box → 96 ÷ 16 = 6
¹⁴₃₅ of the capacity of sand in a box → 14 x 6 = 84 

Mass of the sand and Box F
= 5 u
= 5 x 32
= 160 kg

Mass of the empty box
= 160 - 84
= 76 kg

Answer(s): 76 kg