Container H and Container J were filled completely with sugar. The total mass of ¹₃ of the sugar in Container J and ¹₁₃ of the sugar in Container H was 590 g. If ²₁₃ of the sugar in Container H was poured out, the total mass of the sugar in both containers became 3.21 kg. How much sugar was in

1. Container H in grams?
2. Container J in grams?

(a)
Let the mass of the sugar in Container J be J.
Let the mass of the sugar in Container H be H.

¹₃ J + ¹₁₃ H = 590 --- (1)

Fraction of the sugar left in Container H after ²₁₃ of it was poured out
= 1 - ²₁₃
= ¹¹₁₃

1 kg = 1000 g
3.21 kg = 3210 g

1 J + ¹¹₁₃ H = 3210
1 J = 3210 - ¹¹₁₃ H --- (2)

Make J the same.

(1)_x3
³₃ J + ³₁₃ H = 1770
1 J + ³₁₃ H = 1770
1 J = 1770 - ³₁₃ H --- (3)

(3) = (2) 
1770 - ³₁₃ H = 3210 - ¹¹₁₃ X
¹¹₁₃ H - ³₁₃ H = 3210 - 1770
⁸₁₃ H = 1440
¹₁₃ H = 1440 ÷ 8 = 180

¹³₁₃ H = 13 x 180 = 2340

1 H = 2340

Mass of Container H = 2340 g

(b)
From (1)
¹₃ J + 180 = 590
¹₃ J = 590 - 180 = 410

³₃ J = 3 x 410 = 1230

1 J = 1230

Mass of Container J = 1230 g

Answer(s): (a) 2340 g; (b) 1230 g