Box R and Box S are identical. ⁴₅ of Box R and ³₇ of Box S are filled with sand. The mass of Box S with its contents is ⁸₉ the mass of Box R with its contents. The total mass of the two boxes with their contents is 663 kg. Find the mass of an empty box.
Mass of Box R and its contents = 9 u
Mass of Box S and its contents = 8 u

Total mass of the two boxes with their contents
= 9 u + 8 u
= 17 u

17 u = 663 

1 u = 663 ÷ 17 = 39

Mass of Box R with its concents more than mass of Box S with its contents
= 9 u - 8 u
= 1 u
= 1 x 39
= 39 kg

Fraction of the sand that Box R had more than Box S
= ⁴₅ - ³₇
= ²⁸₃₅ - ¹⁵₃₅
= ¹³₃₅

¹³₃₅ of the capacity of sand in a box → 39
¹₃₅ of the capacity of sand in a box → 39 ÷ 13 = 3
¹⁵₃₅ of the capacity of sand in a box → 15 x 3 = 45 

Mass of the sand and Box S
= 8 u
= 8 x 39
= 312 kg

Mass of the empty box
= 312 - 45
= 267 kg

Answer(s): 267 kg