One application of linear equations is what are termed age problems. When solving age problems, generally the age of two different people (or objects) both now and in the future (or past) are compared. The objective of these problems is usually to find each subject’s current age. Since there can be a lot of information in these problems, a chart can be used to help organize and solve. An example of such a table is below.
Joey is 20 years younger than Becky. In two years, Becky will be twice as old as Joey. Fill in the age problem chart, but do not solve.
Using this last statement gives us the equation to solve: B + 2 = 2 ( B − 18)
Carmen is 12 years older than David. Five years ago, the sum of their ages was 28. How old are they now?
Filling in the chart gives us:
The last statement gives us the equation to solve: Five years ago, the sum of their ages was 28 Therefore, Carmen is David’s age (13) + 12 years = 25 years old.
The sum of the ages of Nicole and Kristin is 32. In two years, Nicole will be three times as old as Kristin. How old are they now?
Filling in the chart gives us:
The last statement gives us the equation to solve: In two years, Nicole will be three times as old as Kristin If Nicole is 25 years old, then Kristin is 32 − 25 = 7 years old.
Louise is 26 years old. Her daughter Carmen is 4 years old. In how many years will Louise be double her daughter’s age?
Filling in the chart gives us:
The last statement gives us the equation to solve: In how many years will Louise be double her daughter’s age? In 18 years, Louise will be twice the age of her daughter. For Questions 1 to 8, write the equation(s) that define the relationship.
Solve Questions 9 to 20.
Answer Key 7.9 Let current age of man be x years old 15 years later, his age is x + 15 Given: 15 + x = 4 (x - 15)15 + x = 4x - 604x - x = 60 + 153x = 75x = 25 Current age = 25 years old
Fifteen years hence a man will be just four times as old as he was $$15$$ years ago. What is his present age?
Given, $$(x+15)=4(x-15)$$ $$\Rightarrow x+15=4x-60$$ $$\Rightarrow 3x=75$$$$\Rightarrow x=25$$ $$\therefore $$ man's present age is $$25$$ years. |