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# Age Word Problems

Age word problems involve finding the age of one or more individuals at a given point in time, based on the information provided in the problem.

• Age Word Problems
• Solved Examples

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## Age Word Problems

Here are some examples of age word problems:

There are no specific formulas for age word problems. However, there are some general steps that can be followed to solve age word problems:

Step 1: Read the problem carefully and identify the unknowns. Usually, the problem will ask for the age of one or more individuals at a specific point in time.

Step 2: Assign variables to represent the unknowns. Let’s say, for example, that the problem asks for the age of person A at a specific point in time. Then we can assign the variable A to represent that age.

Step 3: Use the information provided in the problem to set up one or more equations that relate the unknowns to each other.

Step 4: Solve the equations to find the values of the unknowns.

Step 5: Check your answer by making sure it satisfies all the conditions given in the problem.

It is important to note that age word problems can vary in complexity and may require additional steps or mathematical concepts to solve.

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## Solved Examples

Example 1 :

Lisa is 20 years older than Tom. In 5 years, Lisa’s age will be twice Tom’s age. How old is Tom now?
Solution: Let’s assume Tom’s current age is x. Then Lisa’s current age is x+20. In 5 years, Tom’s age will be x+5 and Lisa’s age will be x+25. According to the problem, Lisa’s age in 5 years will be twice Tom’s age in 5 years. So we can write an equation: x+25 = 2(x+5). Solving this equation, we get x=15. Therefore, Tom is currently 15 years old.

Example 2:

John is twice as old as Mary was when John was as old as Mary is now. If Mary is 20 years old, how old is John?
Solution:Let’s say:
Mary’s current age = M
John’s current age = J

According to the information given, John is twice as old as Mary was when John was as old as Mary is now. This means that the age difference between John and Mary remains constant.

Let’s say x represents the number of years ago when John was as old as Mary is now. At that time, John’s age was (J – x), and Mary’s age was (M – x).

We are given that Mary is currently 20 years old, so M = 20.

From the information above, we can create the following equation:
J = 2(M – x)

Now let’s substitute M with 20 in the equation:
J = 2(20 – x)

Since John’s current age is J and Mary’s current age is M, we know that J = M. Substituting J with M in the equation, we have:
M = 2(20 – x)

Since we know that M = 20, we can solve for x:
20 = 2(20 – x)
20 = 40 – 2x
2x = 40 – 20
2x = 20
x = 10

Now that we have x = 10, we can find John’s current age by substituting x back into the equation J = 2(20 – x):
J = 2(20 – 10)
J = 2(10)
J = 20

Therefore, John is currently 20 years old.

Example 3:

Alex is 5 years older than Bob, and Carol is twice as old as Alex. The sum of their ages is 66. How old is Bob?
Solution: Let’s assume Bob’s current age is x. Then Alex’s current age is x+5, and Carol’s present age is 2(x+5)=2x+10. According to the problem, the sum of their ages is 66. So we can write an equation: x+(x+5)+(2x+10)=66. Solving this equation, we get x=12.75. Therefore, Bob is currently 12.75 years old.

Example 4:

Jane is 10 years younger than John. In 5 years, Jane’s age will be half of John’s age. How old is John now?
Solution: Let’s assume John’s current age is x. Then Jane’s current age is x-10. In 5 years, John’s age will be (x+5)
Jane’s age will be (x-10)+5
Jane’s age will be x+5
According to the problem, Jane’s age will be age on 5 years will half John’s age,
x-5 = 1/2 (x+5)
2(x-5) = (x+5)
2x-10 = x+5
2x -x = 10 + 5
x = 15
John’s age will be 25 years.

## Age Word Problems FAQS

##### What are age word problems?

Age word problems involve finding the age of one or more individuals at a given point in time, based on the information provided in the problem.

##### What are some tips for solving age word problems?

Some tips for solving age word problems include carefully reading the problem, identifying the unknowns, assigning variables to represent the unknowns, using the information provided in the problem to set up equations, solving the equations, and checking your answer.

##### What mathematical concepts are commonly used in age word problems?

Age word problems may involve algebraic equations, linear equations, systems of equations, and other mathematical concepts.

##### How do I know which equation to use for an age word problem?

The equation you use for an age word problem depends on the specific information given in the problem. It is important to carefully read and analyze the problem to determine which equation or equations will be necessary to solve it.

##### How do I check my answer for an age word problem?

You can check your answer for an age word problem by making sure it satisfies all the conditions given in the problem. For example, if the problem states that the sum of the ages of three people is 50, you can check your answer by adding up the ages you found for each person and making sure the total is 50.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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