Solve the problem. See Example.EXAMPLE Dividing a Board into PiecesA project calls for thr...

Solve the problem. See Example.

EXAMPLE Dividing a Board into Pieces

A project calls for three pieces of wood. The longest piece must be twice the length of the middle-sized piece. The shortest piece must be 10 in. shorter than the middle­sized piece. If a board 70 in. long is to be used, how long can each piece be?

Step 1 Read the problem. There will be three answers.

Step 2 Assign a variable. Since the middle-sized piece appears in both pairs of comparisons, let x represent the length, in inches, of the middle-sized piece.

A sketch is helpful here. See FIGURE 2.

FIGURE 2

Step 3 Write an equation.

Step 4 Solve.

Step 5 State the answer. The middle-sized piece is 20 in. long, the longest piece is 2(20) = 40 in. long, and the shortest piece is 20 − 10 = 10 in. long.

Step 6 Check. The lengths sum to 70 in. All problem conditions are satisfied.

The sum of the measures of the angles of any triangle is 180°. In triangle ABC, angles A and B have the same measure, while the measure of angle C is 60° greater than each of A and B. What are the measures of the three angles?