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
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
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 = ?.
Let's break down the information given step-by-step:
Step 1: Avinesh gave his cousin 1/3 of his sticker collection.
Let's assume Avinesh had x stickers at first. He gave away 1/3 of them to his cousin, which means he gave away (1/3)x stickers.
Step 2: Avinesh was left with the remaining stickers.
After giving away (1/3)x stickers to his cousin, Avinesh was left with (2/3)x stickers.
Step 3: Avinesh gave his sister 5/6 of the remainder.
Avinesh gave away 5/6 of (2/3)x stickers to his sister, which means he gave away (5/6) * (2/3) * x stickers.
Step 4: Avinesh was left with 80 stickers.
After giving away (5/6) * (2/3) * x stickers to his sister, Avinesh was left with 80 stickers.
Now we can create an equation to solve for x:
(2/3)x - (5/6) * (2/3) * x = 80
First, let's simplify the equation:
(2/3)x - (10/18)x = 80
Now, let's combine the fractions:
(2/3 - 10/18)x = 80
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 18.
Simplifying the equation further:
[(12 - 10)/18]x = 80
(2/18)x = 80
Now, let's simplify the equation again by dividing both sides by (2/18):
x = (80 / (2/18))
Evaluating the division:
x = 80 * (18/2)
x = 80 * 9
x = 720
Therefore, Avinesh had 720 stickers at first.
To solve this problem, we can break it down into steps:
Step 1: Let's find out how many stickers Avinesh had after giving 1/3 of his collection to his cousin.
Let's assume he had x stickers at first. After giving away 1/3 of his collection, he would be left with (2/3)x stickers.
Step 2: Avinesh then gave 5/6 of the remaining stickers to his sister, which means he was left with 1/6 of the stickers.
So, after giving his sister 5/6 of the remainder, he was left with (1/6) * (2/3)x stickers.
Step 3: We know that he was left with 80 stickers, so we can set up an equation to solve for x:
(1/6) * (2/3)x = 80
To solve this equation, we can multiply both sides by 6/1 to cancel out the fraction:
(2/3)x = 480
Now, we can multiply both sides by 3/2 to isolate x:
x = (480 * 3) / 2
Simplifying this equation gives us:
x = 1440 / 2
x = 720
Therefore, Avinesh had 720 stickers at first.