Sam's age is 1 less than double Shari's age. The sum of their ages is 104. How old is Shari?

Let x = Shari's age and let y = Sam's age. Because Sam's age is 1 less than twice Shari's age this obtains the equation y = 2x - 1. Since the sum of their ages is 104, this provides a second equation of x + y = 104. By substituting the ?rst equation within the second for y, this results in the equation x + 2x - 1 = 104. Combine such as terms on the left side of the equation: 3x - 1 = 104. Add 1 to both sides of the equation: 3x - 1 + 1 = 104 + 1. Simplify: 3x 105. Divide both sides of the equation by 3: 3x/3 = 105/3. The variable, x, is now alone: x = 35. Therefore, Shari's age is 35.