Container X and Container Y were filled completely with pepper. The total mass of ¹₈ of the pepper in Container Y and ¹₁₃ of the pepper in Container X was 430 g. If ²₁₃ of the pepper in Container X was poured out, the total mass of the pepper in both containers became 3.83 kg. How much pepper was in

1. Container X in grams?
2. Container Y in grams?

(a)
Let the mass of the pepper in Container Y be Y.
Let the mass of the pepper in Container X be X.

¹₈ Y + ¹₁₃ X = 430 --- (1)

Fraction of the pepper left in Container X after ²₁₃ of it was poured out
= 1 - ²₁₃
= ¹¹₁₃

1 kg = 1000 g
3.83 kg = 3830 g

1 Y + ¹¹₁₃ X = 3830
1 Y = 3830 - ¹¹₁₃ X --- (2)

Make Y the same.

(1)_x8
⁸₈ Y + ⁸₁₃ X = 3440
1 Y + ⁸₁₃ X = 3440
1 Y = 3440 - ⁸₁₃ X --- (3)

(3) = (2) 
3440 - ⁸₁₃ X = 3830 - ¹¹₁₃ X
¹¹₁₃ X - ⁸₁₃ X = 3830 - 3440
³₁₃ X = 390
¹₁₃ X = 390 ÷ 3 = 130

¹³₁₃ X = 13 x 130 = 1690

1 X = 1690

Mass of Container X = 1690 g

(b)
From (1)
¹₈ Y + 130 = 430
¹₈ Y = 430 - 130 = 300

⁸₈ Y = 8 x 300 = 2400

1 Y = 2400

Mass of Container Y = 2400 g

Answer(s): (a) 1690 g; (b) 2400 g