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
`(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 =
`(1)/(4)x`

Number of marbles after two days =
`(1)/(4)((1)/(4)x)`

=
`((1)/(4))^2x`

Similarly,

Number of marbles after three days =
`((1)/(4))^3x`

Number of marbles after four days =
`((1)/(4))^4x`

Number of marbles after five days =
`((1)/(4))^5x`

=
`(1)/(1024)x`

Since,
`(1)/(1024)` is multiplied with x, therefore, the number of marbles Daniela have left after five days is
`(1)/(1024)` part of original number of marbles.