Box X and Box Y are identical. ³₄ of Box X and ²₇ of Box Y are filled with sand. The mass of Box Y with its contents is ⁵₈ the mass of Box X with its contents. The total mass of the two boxes with their contents is 338 kg. Find the mass of an empty box.
Mass of Box X and its contents = 8 u
Mass of Box Y and its contents = 5 u

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

13 u = 338 

1 u = 338 ÷ 13 = 26

Mass of Box X with its concents more than mass of Box Y with its contents
= 8 u - 5 u
= 3 u
= 3 x 26
= 78 kg

Fraction of the sand that Box X had more than Box Y
= ³₄ - ²₇
= ²¹₂₈ - ⁸₂₈
= ¹³₂₈

¹³₂₈ of the capacity of sand in a box → 78
¹₂₈ of the capacity of sand in a box → 78 ÷ 13 = 6
⁸₂₈ of the capacity of sand in a box → 8 x 6 = 48 

Mass of the sand and Box Y
= 5 u
= 5 x 26
= 130 kg

Mass of the empty box
= 130 - 48
= 82 kg

Answer(s): 82 kg