Container S and Container T were filled completely with sugar. The total mass of ¹₇ of the sugar in Container T and ¹₁₃ of the sugar in Container S was 430 g. If ⁴₁₃ of the sugar in Container S was poured out, the total mass of the sugar in both containers became 3.23 kg. How much sugar was in

1. Container S in grams?
2. Container T in grams?

(a)
Let the mass of the sugar in Container T be T.
Let the mass of the sugar in Container S be S.

¹₇ T + ¹₁₃ S = 430 --- (1)

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

1 kg = 1000 g
3.23 kg = 3230 g

1 T + ⁹₁₃ S = 3230
1 T = 3230 - ⁹₁₃ S --- (2)

Make T the same.

(1)_x7
⁷₇ T + ⁷₁₃ S = 3010
1 T + ⁷₁₃ S = 3010
1 T = 3010 - ⁷₁₃ S --- (3)

(3) = (2) 
3010 - ⁷₁₃ S = 3230 - ⁹₁₃ X
⁹₁₃ S - ⁷₁₃ S = 3230 - 3010
²₁₃ S = 220
¹₁₃ S = 220 ÷ 2 = 110

¹³₁₃ S = 13 x 110 = 1430

1 S = 1430

Mass of Container S = 1430 g

(b)
From (1)
¹₇ T + 110 = 430
¹₇ T = 430 - 110 = 320

⁷₇ T = 7 x 320 = 2240

1 T = 2240

Mass of Container T = 2240 g

Answer(s): (a) 1430 g; (b) 2240 g