Question

I have a rectangular garden. I usually grow cucumbers in 2/3 of my garden, but I want to take 3/4 of the cucumber section to grow

radishes. After I make this change, how much of my whole garden will
be radishes?

Answer 1

`(1)/(2)` of the garden will be radishes.

Explanation:

Given a rectangular garden which grows cucumbers in
`(2)/(3)` of the garden.

`(3)/(4)` of the cucumber section to grow radishes.

To find:

How much of the whole garden will be radishes?

Solution:

Let the total area of the garden =
`x` sq units

Then as per our assumption, total area to grow cucumbers:

`(2x)/(3)` sq units

Cucumber area to grow radishes =
`(3)/(4)` of cucumber area

`= (3)/(4)* (2x)/(3)\\\Rightarrow (x)/(2)\ sq\ units`

Fraction of whole garden to grow radishes = Area to grow radishes divided by whole area of garden

`\Rightarrow ((x)/(2))/(x)\\\\\Rightarrow \bold{(1)/(2)}`

Therefore,
`(1)/(2)` of the garden will be radishes.