A square lobby is to be tiled at Php160 per square meter. if the lobby were 2m narrower and 2m longer, the cost of tiling would be Php35,360. Find the dimension of the lobby.

(pls write the solutions.... thanks)

original size of lobby : x m by x m

new size = x-2 by x+2

area = (x-2)(x+2) = x^2 - 4
cost equation:

160(x^2 - 4) = 35360
x^2 - 4 = 221
x^2 = 225
x = ± 15 , but x must be positive, so

x = 15

To solve this problem, we can set up a system of equations to represent the given information. Let's denote the length of the original lobby as L meters and the width as W meters.

According to the information provided, the square lobby has an area of L x W square meters. Therefore, its area can be expressed as L x W.

We are given that the cost of tiling the square lobby is Php 160 per square meter. So, the cost of tiling the lobby can be expressed as 160 x (L x W).

We are also given that if the lobby were 2 meters narrower and 2 meters longer, the cost of tiling would be Php 35,360. Therefore, the cost of tiling the adjusted lobby can be expressed as 160 x (L+2) x (W-2) = 35,360.

Now we have a system of two equations:

1) L x W = area of the original lobby
2) 160 x (L+2) x (W-2) = 35,360

Let's solve this system of equations to find the dimensions of the lobby:

First, rearrange equation 2 to solve for L in terms of W:
160 x (L+2) x (W-2) = 35,360
(L+2) x (W-2) = 221

Now substitute this expression for L into equation 1:
(L+2) x W = area of the original lobby

Substituting, we have:
(L+2) x W = L x W = area of the original lobby

Now simplify:
2W = area of the original lobby

Substituting back into equation 2:
(L+2) x (W-2) = 221
(2W+2) x (W-2) = 221
2W^2 - 2W - 4W + 4 - 221 = 0
2W^2 - 6W - 217 = 0

Now, we can solve this quadratic equation for W. Factoring the equation or using the quadratic formula, we get:

(W - 19) x (2W + 11) = 0

Setting each factor to zero, we have two possible solutions for W:
W - 19 = 0 or 2W + 11 = 0

If W - 19 = 0, then W = 19. If 2W + 11 = 0, then W = -11/2 (which is not possible for a length).

Therefore, the width of the lobby is W = 19 meters.

Substituting this value back into equation 2,
(2W+2) x (W-2) = 221
(2x19+2) x (19-2) = 221
(38+2) x (17) = 221
40 x 17 = 221
680 = 221

This is not possible, which means there is an error in the given information or the calculations. Please double-check the information provided.