Container F and Container G were filled completely with flour. The total mass of ¹₄ of the flour in Container G and ¹₁₁ of the flour in Container F was 500 g. If ⁵₁₁ of the flour in Container F was poured out, the total mass of the flour in both containers became 2.24 kg. How much flour was in

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

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

¹₄ G + ¹₁₁ F = 500 --- (1)

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

1 kg = 1000 g
2.24 kg = 2240 g

1 G + ⁶₁₁ F = 2240
1 G = 2240 - ⁶₁₁ F --- (2)

Make G the same.

(1)_x4
⁴₄ G + ⁴₁₁ F = 2000
1 G + ⁴₁₁ F = 2000
1 G = 2000 - ⁴₁₁ F --- (3)

(3) = (2) 
2000 - ⁴₁₁ F = 2240 - ⁶₁₁ X
⁶₁₁ F - ⁴₁₁ F = 2240 - 2000
²₁₁ F = 240
¹₁₁ F = 240 ÷ 2 = 120

¹¹₁₁ F = 11 x 120 = 1320

1 F = 1320

Mass of Container F = 1320 g

(b)
From (1)
¹₄ G + 120 = 500
¹₄ G = 500 - 120 = 380

⁴₄ G = 4 x 380 = 1520

1 G = 1520

Mass of Container G = 1520 g

Answer(s): (a) 1320 g; (b) 1520 g