Solve the problem. See Example.EXAMPLE Finding Numbers of Olympic MedalsIn the 2006 Winter...

Solve the problem. See Example.

EXAMPLE Finding Numbers of Olympic Medals

In the 2006 Winter Olympics in Torino, Italy, the United States won 11 more medals than Sweden. The two countries won a total of 39 medals. How many medals did each country win? (Source: U.S. Olympic Committee.)

Step 1 Read the problem carefully. We are given information about the total number of medals and asked to find the number each country won.

Step 2 Assign a variable.

Step 3 Write an equation.

Step 4 Solve the equation.

Step 5 State the answer. The variable x represents the number of medals Sweden won, so Sweden won 14 medals. The number of medals the United States won is

x + 11 = 14 + 11 = 25.

Step 6 Check. Since the United States won 25 medals and Sweden won 14, the total number of medals was 25 + 14 = 39. Because 25 − 14 = 11, the United States won 11 more medals than Sweden. This information agrees with what is given in the problem, so the answer checks.

A one-cup serving of orange juice contains 3 mg less than four times the amount of vitamin C as a one-cup serving of pineapple juice. Servings of the two juices contain a total of 122 mg of vitamin C. How many milligrams of vitamin C are in a serving of each type of juice? (Source: U.S. Agriculture Department.)