Container A and Container B were filled completely with rice flour. The total mass of ¹₆ of the rice flour in Container B and ¹₁₃ of the rice flour in Container A was 430 g. If ⁴₁₃ of the rice flour in Container A was poured out, the total mass of the rice flour in both containers became 2.91 kg. How much rice flour was in

1. Container A in grams?
2. Container B in grams?

(a)
Let the mass of the rice flour in Container B be B.
Let the mass of the rice flour in Container A be A.

¹₆ B + ¹₁₃ A = 430 --- (1)

Fraction of the rice flour left in Container A after ⁴₁₃ of it was poured out
= 1 - ⁴₁₃
= ⁹₁₃

1 kg = 1000 g
2.91 kg = 2910 g

1 B + ⁹₁₃ A = 2910
1 B = 2910 - ⁹₁₃ A --- (2)

Make B the same.

(1)_x6
⁶₆ B + ⁶₁₃ A = 2580
1 B + ⁶₁₃ A = 2580
1 B = 2580 - ⁶₁₃ A --- (3)

(3) = (2) 
2580 - ⁶₁₃ A = 2910 - ⁹₁₃ X
⁹₁₃ A - ⁶₁₃ A = 2910 - 2580
³₁₃ A = 330
¹₁₃ A = 330 ÷ 3 = 110

¹³₁₃ A = 13 x 110 = 1430

1 A = 1430

Mass of Container A = 1430 g

(b)
From (1)
¹₆ B + 110 = 430
¹₆ B = 430 - 110 = 320

⁶₆ B = 6 x 320 = 1920

1 B = 1920

Mass of Container B = 1920 g

Answer(s): (a) 1430 g; (b) 1920 g