Container U and Container V were filled completely with pepper. The total mass of ¹₄ of the pepper in Container V and ¹₁₁ of the pepper in Container U was 580 g. If ⁵₁₁ of the pepper in Container U was poured out, the total mass of the pepper in both containers became 2.7 kg. How much pepper was in

1. Container U in grams?
2. Container V in grams?

(a)
Let the mass of the pepper in Container V be V.
Let the mass of the pepper in Container U be U.

¹₄ V + ¹₁₁ U = 580 --- (1)

Fraction of the pepper left in Container U after ⁵₁₁ of it was poured out
= 1 - ⁵₁₁
= ⁶₁₁

1 kg = 1000 g
2.7 kg = 2700 g

1 V + ⁶₁₁ U = 2700
1 V = 2700 - ⁶₁₁ U --- (2)

Make V the same.

(1)_x4
⁴₄ V + ⁴₁₁ U = 2320
1 V + ⁴₁₁ U = 2320
1 V = 2320 - ⁴₁₁ U --- (3)

(3) = (2) 
2320 - ⁴₁₁ U = 2700 - ⁶₁₁ X
⁶₁₁ U - ⁴₁₁ U = 2700 - 2320
²₁₁ U = 380
¹₁₁ U = 380 ÷ 2 = 190

¹¹₁₁ U = 11 x 190 = 2090

1 U = 2090

Mass of Container U = 2090 g

(b)
From (1)
¹₄ V + 190 = 580
¹₄ V = 580 - 190 = 390

⁴₄ V = 4 x 390 = 1560

1 V = 1560

Mass of Container V = 1560 g

Answer(s): (a) 2090 g; (b) 1560 g