Container X and Container Y were filled completely with sugar. The total mass of ¹₆ of the sugar in Container Y and ¹₁₃ of the sugar in Container X was 560 g. If ⁵₁₃ of the sugar in Container X was poured out, the total mass of the sugar in both containers became 3.6 kg. How much sugar was in

1. Container X in grams?
2. Container Y in grams?

(a)
Let the mass of the sugar in Container Y be Y.
Let the mass of the sugar in Container X be X.

¹₆ Y + ¹₁₃ X = 560 --- (1)

Fraction of the sugar left in Container X after ⁵₁₃ of it was poured out
= 1 - ⁵₁₃
= ⁸₁₃

1 kg = 1000 g
3.6 kg = 3600 g

1 Y + ⁸₁₃ X = 3600
1 Y = 3600 - ⁸₁₃ X --- (2)

Make Y the same.

(1)_x6
⁶₆ Y + ⁶₁₃ X = 3360
1 Y + ⁶₁₃ X = 3360
1 Y = 3360 - ⁶₁₃ X --- (3)

(3) = (2) 
3360 - ⁶₁₃ X = 3600 - ⁸₁₃ X
⁸₁₃ X - ⁶₁₃ X = 3600 - 3360
²₁₃ X = 240
¹₁₃ X = 240 ÷ 2 = 120

¹³₁₃ X = 13 x 120 = 1560

1 X = 1560

Mass of Container X = 1560 g

(b)
From (1)
¹₆ Y + 120 = 560
¹₆ Y = 560 - 120 = 440

⁶₆ Y = 6 x 440 = 2640

1 Y = 2640

Mass of Container Y = 2640 g

Answer(s): (a) 1560 g; (b) 2640 g