### Home > AC > Chapter 12 > Lesson 12.4.2 > Problem12-80

12-80.

If a tile pattern can be described by the equation $y = (x − 1)(x + 2) + x$, 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 211.

2. The number of the figure that contains $6558$ tiles.

Substitute $211$ into the equation for $x$.

Substitute $6558$ into the equation for $y$.

$6558 = (x − 1)(x + 2) + x$

$6558 = x^² + x − 2 + x$

$6558 = x^² + 2x + 2$

Set the equation equal to zero.

$0 = x^² + 2x − 6556$

Factor the expression.

$0 = (x + 82)(x − 80)$

$x=−82$ or $80$

The figure number cannot be negative.

Figure $80$