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.

Venus is 31.2 million mi farther from the sun than Mercury, while Earth is 57 million mi farther from the sun than Mercury. If the total of the distances from these three planets to the sun is 196.2 million mi, how far away from the sun is Mercury? (All distances given here are mean(average) distances.) (Source: The New York Times Almanac.)