Question

Daniela has a container full of marbles. She gives away some of her marbles every day for five days. Each day, she has 1/4 the number of marbles she had a previous day. What fraction of the original number of marbles does Daniela have left after five days?

Answer 1

Given:

Daniela gives away some of her marbles every day for five days.

Each day, she has $\dfrac{1}{4}$ the number of marbles she had a previous day.

To find:

The fraction of the original number of marbles Daniela have left after five days.

Solution:

Let the origin number of marble be x.

Number of marbles after one day = $\dfrac{1}{4}x$

Number of marbles after two days = $\dfrac{1}{4}(\dfrac{1}{4}x)$

                                                        = $(\dfrac{1}{4})^2x$

Similarly,

Number of marbles after three days = $(\dfrac{1}{4})^3x$

Number of marbles after four days = $(\dfrac{1}{4})^4x$

Number of marbles after five days = $(\dfrac{1}{4})^5x$

                                                         = $\dfrac{1}{1024}x$

Since, $\dfrac{1}{1024}$ is multiplied with x, therefore, the number of marbles Daniela have left after five days is $\dfrac{1}{1024}$ part of original number of marbles.