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 …

Question

asked Sep 20, 2021 158k views

1 Answer

Drew Beaupre · Answer 1 · 2021-09-27T09:09:00+0000

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.