Container P and Container Q were filled completely with rice flour. The total mass of ¹₄ of the rice flour in Container Q and ¹₁₃ of the rice flour in Container P was 470 g. If ²₁₃ of the rice flour in Container P was poured out, the total mass of the rice flour in both containers became 2.86 kg. How much rice flour was in

1. Container P in grams?
2. Container Q in grams?

(a)
Let the mass of the rice flour in Container Q be Q.
Let the mass of the rice flour in Container P be P.

¹₄ Q + ¹₁₃ P = 470 --- (1)

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

1 kg = 1000 g
2.86 kg = 2860 g

1 Q + ¹¹₁₃ P = 2860
1 Q = 2860 - ¹¹₁₃ P --- (2)

Make Q the same.

(1)_x4
⁴₄ Q + ⁴₁₃ P = 1880
1 Q + ⁴₁₃ P = 1880
1 Q = 1880 - ⁴₁₃ P --- (3)

(3) = (2) 
1880 - ⁴₁₃ P = 2860 - ¹¹₁₃ X
¹¹₁₃ P - ⁴₁₃ P = 2860 - 1880
⁷₁₃ P = 980
¹₁₃ P = 980 ÷ 7 = 140

¹³₁₃ P = 13 x 140 = 1820

1 P = 1820

Mass of Container P = 1820 g

(b)
From (1)
¹₄ Q + 140 = 470
¹₄ Q = 470 - 140 = 330

⁴₄ Q = 4 x 330 = 1320

1 Q = 1320

Mass of Container Q = 1320 g

Answer(s): (a) 1820 g; (b) 1320 g