Container Y and Container Z were filled completely with flour. The total mass of ¹₅ of the flour in Container Z and ¹₁₃ of the flour in Container Y was 410 g. If ⁴₁₃ of the flour in Container Y was poured out, the total mass of the flour in both containers became 2.49 kg. How much flour was in

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

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

¹₅ Z + ¹₁₃ Y = 410 --- (1)

Fraction of the flour left in Container Y after ⁴₁₃ of it was poured out
= 1 - ⁴₁₃
= ⁹₁₃

1 kg = 1000 g
2.49 kg = 2490 g

1 Z + ⁹₁₃ Y = 2490
1 Z = 2490 - ⁹₁₃ Y --- (2)

Make Z the same.

(1)_x5
⁵₅ Z + ⁵₁₃ Y = 2050
1 Z + ⁵₁₃ Y = 2050
1 Z = 2050 - ⁵₁₃ Y --- (3)

(3) = (2) 
2050 - ⁵₁₃ Y = 2490 - ⁹₁₃ X
⁹₁₃ Y - ⁵₁₃ Y = 2490 - 2050
⁴₁₃ Y = 440
¹₁₃ Y = 440 ÷ 4 = 110

¹³₁₃ Y = 13 x 110 = 1430

1 Y = 1430

Mass of Container Y = 1430 g

(b)
From (1)
¹₅ Z + 110 = 410
¹₅ Z = 410 - 110 = 300

⁵₅ Z = 5 x 300 = 1500

1 Z = 1500

Mass of Container Z = 1500 g

Answer(s): (a) 1430 g; (b) 1500 g