## Elementary Algebra

Let x represent the length of one piece. The length of the other piece is 30 - x. Now, let’s set up a proportion with the ratio given and a ratio which compares the corresponding lengths. $\frac{2}{3}$ = $\frac{x}{(30-x)}$ To solve this equation, we equate the cross products. 2 $\times$ (30 - x) = x $\times$ 3 60 - 2x = 3x 60 = 5x Divide both sides by 5. x = 12 The length of one piece is 12 feet. The length of the other piece is 30 - 12 = 18 feet.