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.

The United States earned 104 medals at the 2012 Summer Olympics. The number of silver medals earned was the same as the number of bronze medals. The number of gold medals was 17 more than the number of silver medals. How many of each kind of medal did the United States earn? (Source: World Almanac and Book of Facts.)