Container W and Container X were filled completely with flour. The total mass of ¹₄ of the flour in Container X and ¹₁₃ of the flour in Container W was 500 g. If ⁵₁₃ of the flour in Container W was poured out, the total mass of the flour in both containers became 2.76 kg. How much flour was in

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

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

¹₄ X + ¹₁₃ W = 500 --- (1)

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

1 kg = 1000 g
2.76 kg = 2760 g

1 X + ⁸₁₃ W = 2760
1 X = 2760 - ⁸₁₃ W --- (2)

Make X the same.

(1)_x4
⁴₄ X + ⁴₁₃ W = 2000
1 X + ⁴₁₃ W = 2000
1 X = 2000 - ⁴₁₃ W --- (3)

(3) = (2) 
2000 - ⁴₁₃ W = 2760 - ⁸₁₃ X
⁸₁₃ W - ⁴₁₃ W = 2760 - 2000
⁴₁₃ W = 760
¹₁₃ W = 760 ÷ 4 = 190

¹³₁₃ W = 13 x 190 = 2470

1 W = 2470

Mass of Container W = 2470 g

(b)
From (1)
¹₄ X + 190 = 500
¹₄ X = 500 - 190 = 310

⁴₄ X = 4 x 310 = 1240

1 X = 1240

Mass of Container X = 1240 g

Answer(s): (a) 2470 g; (b) 1240 g