Container X and Container Y were filled completely with flour. The total mass of ¹₇ of the flour in Container Y and ¹₁₃ of the flour in Container X was 510 g. If ³₁₃ of the flour in Container X was poured out, the total mass of the flour in both containers became 4.11 kg. How much flour was in

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

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

¹₇ Y + ¹₁₃ X = 510 --- (1)

Fraction of the flour left in Container X after ³₁₃ of it was poured out
= 1 - ³₁₃
= ¹⁰₁₃

1 kg = 1000 g
4.11 kg = 4110 g

1 Y + ¹⁰₁₃ X = 4110
1 Y = 4110 - ¹⁰₁₃ X --- (2)

Make Y the same.

(1)_x7
⁷₇ Y + ⁷₁₃ X = 3570
1 Y + ⁷₁₃ X = 3570
1 Y = 3570 - ⁷₁₃ X --- (3)

(3) = (2) 
3570 - ⁷₁₃ X = 4110 - ¹⁰₁₃ X
¹⁰₁₃ X - ⁷₁₃ X = 4110 - 3570
³₁₃ X = 540
¹₁₃ X = 540 ÷ 3 = 180

¹³₁₃ X = 13 x 180 = 2340

1 X = 2340

Mass of Container X = 2340 g

(b)
From (1)
¹₇ Y + 180 = 510
¹₇ Y = 510 - 180 = 330

⁷₇ Y = 7 x 330 = 2310

1 Y = 2310

Mass of Container Y = 2310 g

Answer(s): (a) 2340 g; (b) 2310 g