Container J and Container K were filled completely with pepper. The total mass of ¹₅ of the pepper in Container K and ¹₁₃ of the pepper in Container J was 500 g. If ⁵₁₃ of the pepper in Container J was poured out, the total mass of the pepper in both containers became 2.8 kg. How much pepper was in

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

(a)
Let the mass of the pepper in Container K be K.
Let the mass of the pepper in Container J be J.

¹₅ K + ¹₁₃ J = 500 --- (1)

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

1 kg = 1000 g
2.8 kg = 2800 g

1 K + ⁸₁₃ J = 2800
1 K = 2800 - ⁸₁₃ J --- (2)

Make K the same.

(1)_x5
⁵₅ K + ⁵₁₃ J = 2500
1 K + ⁵₁₃ J = 2500
1 K = 2500 - ⁵₁₃ J --- (3)

(3) = (2) 
2500 - ⁵₁₃ J = 2800 - ⁸₁₃ X
⁸₁₃ J - ⁵₁₃ J = 2800 - 2500
³₁₃ J = 300
¹₁₃ J = 300 ÷ 3 = 100

¹³₁₃ J = 13 x 100 = 1300

1 J = 1300

Mass of Container J = 1300 g

(b)
From (1)
¹₅ K + 100 = 500
¹₅ K = 500 - 100 = 400

⁵₅ K = 5 x 400 = 2000

1 K = 2000

Mass of Container K = 2000 g

Answer(s): (a) 1300 g; (b) 2000 g