Avinesh gave his cousin 1/3 of his sticker collection he gave sister 5/6 the remainder and was left with 80 sticker how many sticker did he have at first

Answer 1

x = sticker he have at first

When he gave his cousin x / 3 of his sticker remainder is:

x - x / 3 = 3 x / 3 - x / 3 = 2 x / 3

He gave sister 5 / 6 the remainder mean :

He gave sister:

5 / 6 ∙ ( 2 x / 3 ) = 5 ∙ 2 x / 6 ∙ 3 = 10 x / 18 = 2 ∙ 5 x / 2 ∙ 9 = 5 x / 9

Total he gave:

x / 3 for his cousin and 5 x / 9 for his sister

Total he gave:

x / 3 + 5 x / 9 = 3 ∙ x / 3 ∙ 3 + 5 x / 9 = 3 x / 9 + 5 x / 9 = 8 x / 9

He remained:

x - 8 x / 9 = 9 x / 9 - 8 x / 9 = x / 9

And was left with 80 sticker mean:

x / 9 = 80

x = 9 ∙ 80 = 720

He did have at first 720 sticker.

Proof:

He gave his cousin x / 3 = 720 / 3 = 240 sticker

Remainder is 720 - 240 = 480 sticker

He gave sister 5 / 6 the remainder.

He gave sister 5 ∙ 480 / 6 = 2400 / 6 = 400 sticker

Total he gave:

240 + 400 = 640 sticker

He was left with 720 - 640 = 80 sticker

Answer 2

He had X stickers at first.

Remainder = x - x/3 = 2x/3 stickers.

2x/3 - 5/6 * 2x/3 = 2x/3(1 - 5/6) = 2x/3(1/6) = x/9.

x/9 = 80,
X = ?.