Question

Radha takes some flowers in a basket and visits three temples one by one. At each temple, she one half of the flowers from the basket. If she is left with \[3\] flowers at the end, find the number of flowers she had in the beginning?

Answer 1

Hint: In the given question we need to determine the number of flowers she had first step is to form the equation from the relations which is provided in the question that after reaching each step she half one of the half of each flowers for example if radha had $a$ flowers then after visiting the temple she will be having $a - \dfrac{a}{2}$ flowers.

Complete step-by-step answer:
Let us first consider that the numbers of flowers radha had in beginning of visiting temple be $a$
As she reaches the first temple she offers one of the half of the flowers from the baskets then in such case we if in first temple radha entered with $a$ flowers then in such case she denoted $a - \dfrac{a}{2}$ flowers in the first temple
Now, the number of flowers she had after visiting the first temple is the subtraction of number of flowers she denoted from the total number of flowers she had before entering the temple
$a - \dfrac{a}{2} = \dfrac{a}{2}$
Now, when she enters the second temple in such a case the total number of flower of flowers she had before entering the second temple will be $\dfrac{a}{2}$ .
Hence, in such case when she denoted one half of the flowers in the temple is represented as
$\dfrac{a}{2} \times \dfrac{1}{2} = \dfrac{a}{4}$
Then in such case the value of total number of flowers she had is
$\dfrac{a}{2} - \dfrac{a}{4} = \dfrac{a}{4}$
Now, when she enters the third temple in such a case the total number of flowers she had before entering the second temple will be $\dfrac{a}{4}$ .
Hence, in such case when she denoted one half of the flowers in the temple is represented as
$\dfrac{a}{4} \times \dfrac{1}{2} = \dfrac{a}{8}$
Then in such case the value of total number of flowers she had is
$\dfrac{a}{4} - \dfrac{a}{8} = \dfrac{a}{8}$
Now, in the last she had three flowers
So,
$\dfrac{a}{8} = 3$
Simplifying the above, we get
$a = 24$

Therefore the girl has a total of 24 flowers in the beginning.

Note: In the required answer it is given that in the end radha is left with three flowers that means we need to substitute the value equal to three such that by simplification we get the required value of total number of flowers she had in the beginning and if we left with the four flowers then we substitute the same equation equal to four.