Container L and Container M were filled completely with sugar. The total mass of ¹₇ of the sugar in Container M and ¹₁₁ of the sugar in Container L was 590 g. If ²₁₁ of the sugar in Container L was poured out, the total mass of the sugar in both containers became 4.53 kg. How much sugar was in

1. Container L in grams?
2. Container M in grams?

(a)
Let the mass of the sugar in Container M be M.
Let the mass of the sugar in Container L be L.

¹₇ M + ¹₁₁ L = 590 --- (1)

Fraction of the sugar left in Container L after ²₁₁ of it was poured out
= 1 - ²₁₁
= ⁹₁₁

1 kg = 1000 g
4.53 kg = 4530 g

1 M + ⁹₁₁ L = 4530
1 M = 4530 - ⁹₁₁ L --- (2)

Make M the same.

(1)_x7
⁷₇ M + ⁷₁₁ L = 4130
1 M + ⁷₁₁ L = 4130
1 M = 4130 - ⁷₁₁ L --- (3)

(3) = (2) 
4130 - ⁷₁₁ L = 4530 - ⁹₁₁ X
⁹₁₁ L - ⁷₁₁ L = 4530 - 4130
²₁₁ L = 400
¹₁₁ L = 400 ÷ 2 = 200

¹¹₁₁ L = 11 x 200 = 2200

1 L = 2200

Mass of Container L = 2200 g

(b)
From (1)
¹₇ M + 200 = 590
¹₇ M = 590 - 200 = 390

⁷₇ M = 7 x 390 = 2730

1 M = 2730

Mass of Container M = 2730 g

Answer(s): (a) 2200 g; (b) 2730 g