Container X and Container Y were filled completely with bread flour. The total mass of ¹₇ of the bread flour in Container Y and ¹₁₃ of the bread flour in Container X was 580 g. If ²₁₃ of the bread flour in Container X was poured out, the total mass of the bread flour in both containers became 4.74 kg. How much bread flour was in

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

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

¹₇ Y + ¹₁₃ X = 580 --- (1)

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

1 kg = 1000 g
4.74 kg = 4740 g

1 Y + ¹¹₁₃ X = 4740
1 Y = 4740 - ¹¹₁₃ X --- (2)

Make Y the same.

(1)_x7
⁷₇ Y + ⁷₁₃ X = 4060
1 Y + ⁷₁₃ X = 4060
1 Y = 4060 - ⁷₁₃ X --- (3)

(3) = (2) 
4060 - ⁷₁₃ X = 4740 - ¹¹₁₃ X
¹¹₁₃ X - ⁷₁₃ X = 4740 - 4060
⁴₁₃ X = 680
¹₁₃ X = 680 ÷ 4 = 170

¹³₁₃ X = 13 x 170 = 2210

1 X = 2210

Mass of Container X = 2210 g

(b)
From (1)
¹₇ Y + 170 = 580
¹₇ Y = 580 - 170 = 410

⁷₇ Y = 7 x 410 = 2870

1 Y = 2870

Mass of Container Y = 2870 g

Answer(s): (a) 2210 g; (b) 2870 g