Box X and Box Y are identical. ⁶₇ of Box X and ²₅ of Box Y are filled with sand. The mass of Box Y with its contents is ⁹₁₀ the mass of Box X with its contents. The total mass of the two boxes with their contents is 912 kg. Find the mass of an empty box.
Mass of Box X and its contents = 10 u
Mass of Box Y and its contents = 9 u

Total mass of the two boxes with their contents
= 10 u + 9 u
= 19 u

19 u = 912 

1 u = 912 ÷ 19 = 48

Mass of Box X with its concents more than mass of Box Y with its contents
= 10 u - 9 u
= 1 u
= 1 x 48
= 48 kg

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

¹⁶₃₅ of the capacity of sand in a box → 48
¹₃₅ of the capacity of sand in a box → 48 ÷ 16 = 3
¹⁴₃₅ of the capacity of sand in a box → 14 x 3 = 42 

Mass of the sand and Box Y
= 9 u
= 9 x 48
= 432 kg

Mass of the empty box
= 432 - 42
= 390 kg

Answer(s): 390 kg