Container G and Container H were filled completely with flour. The total mass of ¹₃ of the flour in Container H and ¹₁₁ of the flour in Container G was 590 g. If ⁵₁₁ of the flour in Container G was poured out, the total mass of the flour in both containers became 2.28 kg. How much flour was in

1. Container G in grams?
2. Container H in grams?

(a)
Let the mass of the flour in Container H be H.
Let the mass of the flour in Container G be G.

¹₃ H + ¹₁₁ G = 590 --- (1)

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

1 kg = 1000 g
2.28 kg = 2280 g

1 H + ⁶₁₁ G = 2280
1 H = 2280 - ⁶₁₁ G --- (2)

Make H the same.

(1)_x3
³₃ H + ³₁₁ G = 1770
1 H + ³₁₁ G = 1770
1 H = 1770 - ³₁₁ G --- (3)

(3) = (2) 
1770 - ³₁₁ G = 2280 - ⁶₁₁ X
⁶₁₁ G - ³₁₁ G = 2280 - 1770
³₁₁ G = 510
¹₁₁ G = 510 ÷ 3 = 170

¹¹₁₁ G = 11 x 170 = 1870

1 G = 1870

Mass of Container G = 1870 g

(b)
From (1)
¹₃ H + 170 = 590
¹₃ H = 590 - 170 = 420

³₃ H = 3 x 420 = 1260

1 H = 1260

Mass of Container H = 1260 g

Answer(s): (a) 1870 g; (b) 1260 g