Two identical buckets W and X contained some water. Bucket W was ¹₈ filled and Bucket X was ¹₉ filled. The ratio of the total mass of Bucket W and the water in it to the total mass of Bucket X and the water in it was 13 : 12. The total mass of the two buckets and the water they contained was 7500 g. What is the mass of an empty bucket?
Mass of Bucket W and the water inside = 13 u
Mass of Bucket X and the water inside = 12 u

Total mass of the two buckets and the water inside them
= 13 u + 12 u
= 25 u

25 u = 7500

1 u = 7500 ÷ 25 = 300

Mass of Bucket W and the water in it more than mass of Bucket X and the water in it 
= 13 u - 12 u
= 1 u

Fraction of the water that Bucket W had more than Bucket X 
= ¹₈ - ¹₉
= ⁹₇₂ - ⁸₇₂
= ¹₇₂ 

¹₇₂ of the water capacity → 1 u
⁸₇₂ of the water capacity → 8 x 1 u = 8 u

Mass of an empty bucket
= 12 u - 8 u
= 4 u
= 4 x 300
= 1200 g

Answer(s): 1200 g