Container B and Container C were filled completely with rice flour. The total mass of ¹₃ of the rice flour in Container C and ¹₁₃ of the rice flour in Container B was 580 g. If ⁵₁₃ of the rice flour in Container B was poured out, the total mass of the rice flour in both containers became 2.64 kg. How much rice flour was in

1. Container B in grams?
2. Container C in grams?

(a)
Let the mass of the rice flour in Container C be C.
Let the mass of the rice flour in Container B be B.

¹₃ C + ¹₁₃ B = 580 --- (1)

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

1 kg = 1000 g
2.64 kg = 2640 g

1 C + ⁸₁₃ B = 2640
1 C = 2640 - ⁸₁₃ B --- (2)

Make C the same.

(1)_x3
³₃ C + ³₁₃ B = 1740
1 C + ³₁₃ B = 1740
1 C = 1740 - ³₁₃ B --- (3)

(3) = (2) 
1740 - ³₁₃ B = 2640 - ⁸₁₃ X
⁸₁₃ B - ³₁₃ B = 2640 - 1740
⁵₁₃ B = 900
¹₁₃ B = 900 ÷ 5 = 180

¹³₁₃ B = 13 x 180 = 2340

1 B = 2340

Mass of Container B = 2340 g

(b)
From (1)
¹₃ C + 180 = 580
¹₃ C = 580 - 180 = 400

³₃ C = 3 x 400 = 1200

1 C = 1200

Mass of Container C = 1200 g

Answer(s): (a) 2340 g; (b) 1200 g