Question

50 POINTS!!!! Need help in number 4

Answer 1

Hi,

Explanation:

First, we calculate the area of the orchard.
The remaining 69 acres are 1-3/8-1/6=1-9/24-4/24=11/24 of the orchard.
The orchard has an area of 69*24/11= 1656/11 acres.

The land has an area of 1656/11*3=4968/11 acres =1827772,3636... m²

Answer 2

552 acres

Explanation:

Let x be the total area of the land.

Given 1/3 of the land is used for oranges, 3/8 for pears, 1/6 for apples, and the remaining 68 acres is for grapes, then we can write the following equation:

`(1)/(3)x+(3)/(8)x+(1)/(6)x+69=x`

To find the total area of the land, we need to solve the equation for x.

As the fractions have different denominators, we first need to convert the fractions into equivalent fractions with the same denominator.

The lowest common multiple of the denominators 3, 8 and 6 is 24.

Therefore, multiply the numerator and denominator of each fraction by the same number so that the denominator becomes 24:

`(1\cdot 8)/(3 \cdot 8)x+(3\cdot 3)/(8\cdot 3)x+(1\cdot 4)/(6\cdot 4)x+69=x`

`(8)/(24)x+(9)/(24)x+(4)/(24)x+69=x`

Now the fractions have the same denominator, we can add them by simply adding their numerators:

`(8+9+4)/(24)x+69=x`

`(21)/(24)x+69=x`

Reduce the fraction to its simplest form by dividing the numerator and denominator by the common factor of 3:

`(21 / 3)/(24/ 3)x+69=x`

`(7)/(8)x+69=x`

Rewrite x as a fraction with denominator 8 (remembering that a number divided by itself equals one):

`(7)/(8)x+69=(8)/(8)x`

Subtract 7/8 x from both sides of the equation:

`(7)/(8)x+69-(7)/(8)x=(8)/(8)x-(7)/(8)x`

`69=(8-7)/(8)x`

`69=(1)/(8)x`

Multiply both sides of the equation by 8:

`69\cdot 8=(1)/(8)x \cdot 8`

`552=x`

`x=552`

Therefore, the total area of the land is 552 acres.