Container J and Container K were filled completely with bread flour. The total mass of ¹₈ of the bread flour in Container K and ¹₁₃ of the bread flour in Container J was 590 g. If ²₁₃ of the bread flour in Container J was poured out, the total mass of the bread flour in both containers became 5.2 kg. How much bread flour was in

1. Container J in grams?
2. Container K in grams?

(a)
Let the mass of the bread flour in Container K be K.
Let the mass of the bread flour in Container J be J.

¹₈ K + ¹₁₃ J = 590 --- (1)

Fraction of the bread flour left in Container J after ²₁₃ of it was poured out
= 1 - ²₁₃
= ¹¹₁₃

1 kg = 1000 g
5.2 kg = 5200 g

1 K + ¹¹₁₃ J = 5200
1 K = 5200 - ¹¹₁₃ J --- (2)

Make K the same.

(1)_x8
⁸₈ K + ⁸₁₃ J = 4720
1 K + ⁸₁₃ J = 4720
1 K = 4720 - ⁸₁₃ J --- (3)

(3) = (2) 
4720 - ⁸₁₃ J = 5200 - ¹¹₁₃ X
¹¹₁₃ J - ⁸₁₃ J = 5200 - 4720
³₁₃ J = 480
¹₁₃ J = 480 ÷ 3 = 160

¹³₁₃ J = 13 x 160 = 2080

1 J = 2080

Mass of Container J = 2080 g

(b)
From (1)
¹₈ K + 160 = 590
¹₈ K = 590 - 160 = 430

⁸₈ K = 8 x 430 = 3440

1 K = 3440

Mass of Container K = 3440 g

Answer(s): (a) 2080 g; (b) 3440 g