Bob is 2 years from being double as old as Ellen. The sum of twice Bob's age and three times Ellen's age is 66. How old is Ellen?
Let x = Ellen's age and let y = Bob's age. Since Bob is 2 years from being double as old as Ellen, than y = 2x - 2. The sum of twice Bob's age and three times Ellen's age is 66 and provides a second equation of 2y + 3x = 66. Substituting the ?rst equation for y into the second equation results in 2(2x - 2) + 3x = 66. Use the distributive property on the left side of the equation: 4x - 4 + 3x = 66; combine such as terms on the left side of the equation: 7x - 4 = 66. Add 4 to both sides of the equation: 7x - 4 + 4 = 66 + 4. Simplify: 7x = 70. Divide both sides of the equation by 7: 7x/7 = 70/7. The variable, x, is now alone: x = 10. Thus, Ellen is 10 years old.