Solve the problem. See ExampleEXAMPLE Dividing a Board into PiecesA project calls for thre...

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 must each piece be?

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

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

A sketch is helpful. See FIGURE figure 3.

FIGURE figure 3

Step 3 Write an equation.

Step 4

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.

A three-foot-long deli sandwich must be split into three pieces so that the middle piece is twice as long as the shortest piece and the shortest piece is 8 in. shorter than the longest piece. How long should the three pieces be?