Question

Myra is putting together a puzzle such that every 5 days she places one quarter of the remaining pieces into the puzzle. If she started with a 800 piece puzzle, how many pieces are left to be placed after 23 days? Show the work that leads to your answer

Answer 1

Given:

Initial number of pieces Myra have = 800.

Every 5 days she places one quarter of the remaining pieces into the puzzle.

To find:

The number of remaining pieces after 23 days.

Solution:

Initial number of pieces Myra have = 800.

Every 5 days she places one quarter of the remaining pieces into the puzzle.

It means, she will place the puzzles on 5,10,15,20,25,.. days. she will place the puzzle 4 times before 23 days.

The number of remaining pieces decreasing by
`(1)/(4)`.

Formula for number of remaining pieces is

`y=a_0(1-r)^t`

where,
`a_0` is the initial value, r is decreasing rate and t is time.

Putting
`a_0=800,r=(1)/(4)` and t=4, we get

`y=800(1-(1)/(4))^4`

`y=800((3)/(4))^4`

`y=800(0.75)^4`

`y=800(0.31640625 )`

`y=253.125`

Approximate the value to the nearest whole number.

`y\approx 253`

Therefore, the number of remaining pieces is 253.