Two identical buckets W and X contained some water. Bucket W was ¹₃ filled and Bucket X was ¹₄ 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 9 : 8. The total mass of the two buckets and the water they contained was 2210 g. What is the mass of an empty bucket?
Mass of Bucket W and the water inside = 9 u
Mass of Bucket X and the water inside = 8 u

Total mass of the two buckets and the water inside them
= 9 u + 8 u
= 17 u

17 u = 2210

1 u = 2210 ÷ 17 = 130

Mass of Bucket W and the water in it more than mass of Bucket X and the water in it 
= 9 u - 8 u
= 1 u

Fraction of the water that Bucket W had more than Bucket X 
= ¹₃ - ¹₄
= ⁴₁₂ - ³₁₂
= ¹₁₂ 

¹₁₂ of the water capacity → 1 u
³₁₂ of the water capacity → 3 x 1 u = 3 u

Mass of an empty bucket
= 8 u - 3 u
= 5 u
= 5 x 130
= 650 g

Answer(s): 650 g