Container X and Container Y were filled completely with flour. The total mass of
15 of the flour in Container Y and
113 of the flour in Container X was 500 g. If
313 of the flour in Container X was poured out, the total mass of the flour in both containers became 3.45 kg. How much flour was in
- Container X in grams?
- Container Y in grams?
(a)
Let the mass of the flour in Container Y be Y.
Let the mass of the flour in Container X be X.
15 Y +
113 X = 500 --- (1)
Fraction of the flour left in Container X after
313 of it was poured out
= 1 -
313 =
1013 1 kg = 1000 g
3.45 kg = 3450 g
1 Y +
1013 X = 3450
1 Y = 3450 -
1013 X --- (2)
Make Y the same.
(1)
x5 55 Y +
513 X = 2500
1 Y +
513 X = 2500
1 Y = 2500 -
513 X --- (3)
(3) = (2)
2500 -
513 X = 3450 -
1013 X
1013 X -
513 X = 3450 - 2500
513 X = 950
113 X = 950 ÷ 5 = 190
1313 X = 13 x 190 = 2470
1 X = 2470
Mass of Container X = 2470 g
(b)
From (1)
15 Y + 190 = 500
15 Y = 500 - 190 = 310
55 Y = 5 x 310 = 1550
1 Y = 1550
Mass of Container Y = 1550 g
Answer(s): (a) 2470 g; (b) 1550 g