Question 883353: When we use square tiles of unknown length to cover a floor, we require 128 tiles. If the side of the tile is decreased by 2 cm, we require 200 tiles. Find the side of the larger tile.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! When we use square tiles of unknown length to cover a floor, we require 128 tiles.
If the side of the tile is decreased by 2 cm, we require 200 tiles.
Find the side of the larger tile.
:
let x = side of the larger tile
then
(x-2) = side of the smaller
then
128x^2 = size of the floor
:
The equation
200(x-2)^2 = 128x^2
:
Simplify, divide by 8
25(x-2)^2 = 16x^2
:
FOIL (x-2)(x-2)
25(x^2 - 4x + 4) = 16x^2
25x^2 - 100x + 100 = 16x^2
25x^2 - 16x^2 - 100x + 100 = 0
:
A quadratic equation
9x^2 - 100x + 100 = 0
:
you can use the quadratic formula here, but this will factor to:
(9x-10)(x-10) = 0
x = 10 cm is the reasonable answer
:
:
See if that works
Find the area of the floor: 128(10^2) = 12800 sq/cm
Find the area of the smaller tile
8*8 = 64 sq/cm
Find how many of these tiles are required to cover 2800sq/cm
12800/64 = 200 tiles
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