Lucy suzan and pamela own 17 square units of shamba lucy owns 2/3 of what suzan owns and pamela owns 1/3 of what lucy owns what fraction of whole shamba does each owns
Susan: X sq. units.
Lucy: 2x/3 sq. units.
Pamela: 1/3 * 2x/3 = 2x/9 sq. units.
x + 2x/3 + 2x/9 = 17.
9x/9 + 6x/9 + 2x/9 = 17
17x/9 = 17
X = 9 sq. units.
2x/3 =
2x/9 =
Let's break down the information given step-by-step:
1. Total area of the shamba = 17 square units.
2. Let's assume that Suzan owns "x" square units of the shamba. According to the given information, Lucy owns 2/3 of what Suzan owns. Therefore, Lucy owns (2/3) * x = (2x/3) square units.
3. Additionally, Pamela owns 1/3 of what Lucy owns. Therefore, Pamela owns (1/3) * (2x/3) = (2x/9) square units.
4. We can sum up the areas owned by all three to equal the total area of the shamba:
x + (2x/3) + (2x/9) = 17
Now, let's solve for "x" to find out the area each person owns.
Multiplying through by the denominator to eliminate fractions:
9x + 6x + 2x = 17 * 9
17x = 153
Dividing both sides by 17:
x = 153/17
Simplifying:
x = 9
Therefore, Suzan owns 9 square units, Lucy owns (2/3) * 9 = 6 square units, and Pamela owns (2/9) * 9 = 2 square units.
So, Suzan owns 9/17 of the shamba, Lucy owns 6/17, and Pamela owns 2/17.
To find the fraction of the whole shamba that each person owns, we need to calculate the fractions that represent their shares.
Let's start with Suzan's share. We know that Lucy owns 2/3 of what Suzan owns, which means Lucy's share is 2/3 * Suzan's share. We're given that the total area owned by the three of them is 17 square units. Therefore, Suzan's share can be represented by x, and Lucy's share is (2/3)x.
We also know that Pamela owns 1/3 of what Lucy owns. Therefore, Pamela's share can be represented as (1/3)*(2/3)x.
To find the total area, we sum up the shares of all three:
x + (2/3)x + (1/3)*(2/3)x = 17
Now we can solve for x.
To simplify the equation, we make the denominators common:
(3/3)x + (2/3)x + (2/9)x = 17
(9/9)x + (6/9)x + (2/9)x = 17
(17/9)x = 17
Now we can solve for x:
x = 17 * (9/17)
x = 9
So, Suzan's share is 9 square units.
Now we can find the shares for Lucy and Pamela:
Lucy's share = (2/3) * 9 = 6 square units
Pamela's share = (1/3) * (2/3) * 9 = 2 square units
Finally, let's calculate the fraction of the whole shamba owned by each person:
Suzan's fraction = Suzan's share / Total area = 9/17
Lucy's fraction = Lucy's share / Total area = 6/17
Pamela's fraction = Pamela's share / Total area = 2/17
Therefore, Suzan owns 9/17 of the shamba, Lucy owns 6/17, and Pamela owns 2/17.