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Word Problems Involving Ages
Solving Age Word Problems Using Algebra
More Algebra Lessons
Age problems are algebra word problems that deal with the ages of people currently, in the past or in the future. The ages of the people are compared and usually the objective would be to find their current age.
Printable & Online Algebra Worksheets
If the problem involves a single person, then it is similar to an Integer Problem. Read the problem carefully to determine the relationship between the numbers. See example involving a single person.
In these lessons, we will learn how to solve age problems that involve the ages of two or more people.
Solving age word problems involving 3 people can seem complex, but using a table to organize the information makes it much easier. This is shown in the following age word problems that involve more than one person.
The following diagram shows how to solve an age word problem involving three people. Scroll down the page for more examples and solutions.
Example:
John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John will be
three times as old as Alice. How old is Peter now?
Solution:
Step 1: Set up a table.
Step 2: Fill in the table with information given in the question.
John is twice as old as his friend Peter. Peter is 5 years older than Alice. In 5 years, John
will be three times as old as Alice. How old is Peter now?
Let x be Peter’s age now. Add 5 to get the ages in 5 yrs.
Write the new relationship in an equation using the ages in 5 yrs.
In 5 years, John will be three times as old as Alice.
2x + 5 = 3(x – 5 + 5)
2x + 5 = 3x
Isolate variable x
x = 5
Answer: Peter is now 5 years old.
Example:
John’s father is 5 times older than John and John is twice as old as his sister Alice. In two
years time, the sum of their ages will be 58. How old is John now?
Solution:
Step 1: Set up a table.
Step 2: Fill in the table with information given in the question.
John’s father is 5 times older than John and John is twice as old as his sister Alice.
In two years time, the sum of their ages will be 58. How old is John now?
Let x be John’s age now. Add 2 to get the ages in 2 yrs.
Write the new relationship in an equation using the ages in 2 yrs.
In two years time, the sum of their ages will be 58.
Answer: John is now 8 years old.
Example:
Mary is 3 times as old as her son. In 12 years, Mary’s age will be one year less than twice her son’s
age. Find their ages now.
Note that this problem requires a chart to organize the information. The rows of the chart can be labeled as Mary and Son, and the columns of the chart can be labeled as “age now” and “age in 12 years”. The chart is then used to set up the equation.
Examples:
Examples:
Examples:
Example: Zack is four times as old as Salman. Zack is also three years older than Salman. How old is Zack?
Examples For Practise:
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