Container P and Container Q were filled completely with sugar. The total mass of ¹₄ of the sugar in Container Q and ¹₁₁ of the sugar in Container P was 580 g. If ³₁₁ of the sugar in Container P was poured out, the total mass of the sugar in both containers became 3.12 kg. How much sugar was in

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

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

¹₄ Q + ¹₁₁ P = 580 --- (1)

Fraction of the sugar left in Container P after ³₁₁ of it was poured out
= 1 - ³₁₁
= ⁸₁₁

1 kg = 1000 g
3.12 kg = 3120 g

1 Q + ⁸₁₁ P = 3120
1 Q = 3120 - ⁸₁₁ P --- (2)

Make Q the same.

(1)_x4
⁴₄ Q + ⁴₁₁ P = 2320
1 Q + ⁴₁₁ P = 2320
1 Q = 2320 - ⁴₁₁ P --- (3)

(3) = (2) 
2320 - ⁴₁₁ P = 3120 - ⁸₁₁ X
⁸₁₁ P - ⁴₁₁ P = 3120 - 2320
⁴₁₁ P = 800
¹₁₁ P = 800 ÷ 4 = 200

¹¹₁₁ P = 11 x 200 = 2200

1 P = 2200

Mass of Container P = 2200 g

(b)
From (1)
¹₄ Q + 200 = 580
¹₄ Q = 580 - 200 = 380

⁴₄ Q = 4 x 380 = 1520

1 Q = 1520

Mass of Container Q = 1520 g

Answer(s): (a) 2200 g; (b) 1520 g