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

Answer:

$\frac{1}{2}$ of the garden will be radishes.

Step-by-step explanation:

Given a rectangular garden which grows cucumbers in $\frac{2}{3}$ of the garden.

$\frac{3}{4}$ 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:

$\frac{2x}{3}$ sq units

Cucumber area to grow radishes = $\frac{3}{4}$ of cucumber area

$= \dfrac{3}{4}\times \dfrac{2x}{3}\\\Rightarrow \dfrac{x}{2}\ sq\ units$

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

$\Rightarrow \dfrac{\frac{x}{2}}{x}\\\\\Rightarrow \bold{\dfrac{1}{2}}$

Therefore, $\frac{1}{2}$ of the garden will be radishes.