### Home > AC > Chapter 12 > Lesson 12.4.2 > Problem12-73

12-73.

If a tile pattern can be described by the equation $y=\left(x-1\right)\left(x+1\right)+x+2$, where $x$ represents the figure number and $y$ represents the number of tiles, find each of the following.

1. The number of tiles in Figure $307$.

Substitute 307 into the equation for $x$.

$y=\left(307-1\right)\left(307+1\right)+307+2$

Solve for $y$.

$y = 94{,}557$

2. The number of the figure that contains $169{,}333$ tiles.

Set $y = 169{,}333$.

$169,333=\left(x-1\right)\left(x+1\right)+x+2$

Solve for $x$.