David bought a bag of soil to do gardening. He kept 4/9 of it for his own use. Then he scooped out 1.5 kg of the soil for his brother and 2/7 of the remainder for his sister. He gave the rest to his mother. 1/5 of his mother’s share was 250 g. What was the mass of the bag of soil David bought?

Answer 1

Suppose that David bought x g soil.
So he kept 4/9x for his own use.
then scooped out 1.5 kg.
So now the remainder is x - 4/9x - 1.5 kg
= 5/9x - 1500g { 1 kg = 1000g}

So he gave 2/7 (5/9x - 1500g) for his
sister.

So the rest for his mother is
(1 - 2/7) (5/9x - 1500 g).
So 1/5 * (1 - 2/7) (5/9x - 1500 g) = 250 g.
1/7(5/9x - 1500 g) = 250 g
1/9x - 1500 g = 1750 g
5/9x = 3250 g
x = 5850 g
= 5.85 kg