Container J and Container K were filled completely with flour. The total mass of ¹₃ of the flour in Container K and ¹₁₁ of the flour in Container J was 530 g. If ⁵₁₁ of the flour in Container J was poured out, the total mass of the flour in both containers became 2.04 kg. How much flour was in

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

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

¹₃ K + ¹₁₁ J = 530 --- (1)

Fraction of the flour left in Container J after ⁵₁₁ of it was poured out
= 1 - ⁵₁₁
= ⁶₁₁

1 kg = 1000 g
2.04 kg = 2040 g

1 K + ⁶₁₁ J = 2040
1 K = 2040 - ⁶₁₁ J --- (2)

Make K the same.

(1)_x3
³₃ K + ³₁₁ J = 1590
1 K + ³₁₁ J = 1590
1 K = 1590 - ³₁₁ J --- (3)

(3) = (2) 
1590 - ³₁₁ J = 2040 - ⁶₁₁ X
⁶₁₁ J - ³₁₁ J = 2040 - 1590
³₁₁ J = 450
¹₁₁ J = 450 ÷ 3 = 150

¹¹₁₁ J = 11 x 150 = 1650

1 J = 1650

Mass of Container J = 1650 g

(b)
From (1)
¹₃ K + 150 = 530
¹₃ K = 530 - 150 = 380

³₃ K = 3 x 380 = 1140

1 K = 1140

Mass of Container K = 1140 g

Answer(s): (a) 1650 g; (b) 1140 g