Container U and Container V were filled completely with flour. The total mass of ¹₅ of the flour in Container V and ¹₁₃ of the flour in Container U was 560 g. If ²₁₃ of the flour in Container U was poured out, the total mass of the flour in both containers became 3.94 kg. How much flour was in

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

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

¹₅ V + ¹₁₃ U = 560 --- (1)

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

1 kg = 1000 g
3.94 kg = 3940 g

1 V + ¹¹₁₃ U = 3940
1 V = 3940 - ¹¹₁₃ U --- (2)

Make V the same.

(1)_x5
⁵₅ V + ⁵₁₃ U = 2800
1 V + ⁵₁₃ U = 2800
1 V = 2800 - ⁵₁₃ U --- (3)

(3) = (2) 
2800 - ⁵₁₃ U = 3940 - ¹¹₁₃ X
¹¹₁₃ U - ⁵₁₃ U = 3940 - 2800
⁶₁₃ U = 1140
¹₁₃ U = 1140 ÷ 6 = 190

¹³₁₃ U = 13 x 190 = 2470

1 U = 2470

Mass of Container U = 2470 g

(b)
From (1)
¹₅ V + 190 = 560
¹₅ V = 560 - 190 = 370

⁵₅ V = 5 x 370 = 1850

1 V = 1850

Mass of Container V = 1850 g

Answer(s): (a) 2470 g; (b) 1850 g