Container X and Container Y were filled completely with flour. The total mass of ¹₄ of the flour in Container Y and ¹₁₃ of the flour in Container X was 530 g. If ⁵₁₃ of the flour in Container X was poured out, the total mass of the flour in both containers became 2.64 kg. How much flour was in

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

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

¹₄ Y + ¹₁₃ X = 530 --- (1)

Fraction of the flour left in Container X after ⁵₁₃ of it was poured out
= 1 - ⁵₁₃
= ⁸₁₃

1 kg = 1000 g
2.64 kg = 2640 g

1 Y + ⁸₁₃ X = 2640
1 Y = 2640 - ⁸₁₃ X --- (2)

Make Y the same.

(1)_x4
⁴₄ Y + ⁴₁₃ X = 2120
1 Y + ⁴₁₃ X = 2120
1 Y = 2120 - ⁴₁₃ X --- (3)

(3) = (2) 
2120 - ⁴₁₃ X = 2640 - ⁸₁₃ X
⁸₁₃ X - ⁴₁₃ X = 2640 - 2120
⁴₁₃ X = 520
¹₁₃ X = 520 ÷ 4 = 130

¹³₁₃ X = 13 x 130 = 1690

1 X = 1690

Mass of Container X = 1690 g

(b)
From (1)
¹₄ Y + 130 = 530
¹₄ Y = 530 - 130 = 400

⁴₄ Y = 4 x 400 = 1600

1 Y = 1600

Mass of Container Y = 1600 g

Answer(s): (a) 1690 g; (b) 1600 g