In real-life scenarios, we often encounter situations where understanding the relationship between different time points can help us solve problems. This is especially true when it comes to age-related questions. Let's explore how to approach such problems using algebraic equations and solve a few examples.

Introduction to Age Equations

Age equations involve the use of algebra to determine the age of a person based on the given conditions. These equations can often be complex and require careful manipulation to arrive at a solution. In this article, we will walk through several examples to see how age equations can be solved.

Example 1: A Girl's Age

Let's consider a problem where a girl's age is determined based on future and past conditions:

Problem: A girl is currently x years old. If her age in 12 years will be 4 times her age 6 years ago, how old is the girl?

Solution:

Let's denote the girl's current age as x.

Her age in 12 years will be x 12.

Her age 6 years ago was x - 6.

The equation based on the given information is:

x 12 4(x - 6)

Now, let's solve the equation step by step:

Expand the right side: x 12 4x - 24 Rearrange the equation to isolate x: x 12 24 4x 36 3x Divide both sides by 3: x 12

Therefore, the girl is 12 years old.

Example 2: Your Age

Let's take a different example where we use the same methodology:

Problem: If your age in 7 years will be 4 times your age 8 years ago, how old are you now?

Solution:

Let's denote your current age as x.

Your age in 7 years will be x 7.

Your age 8 years ago was x - 8.

The equation based on the given information is:

x 7 4(x - 8)

Now, let's solve the equation step by step:

Expand the right side: x 7 4x - 32 Rearrange the equation to isolate x: x 7 32 4x 39 3x Divide both sides by 3: x 13

Therefore, you are 13 years old.

Example 3: Inusah's Age

Let's look at another example to further illustrate the concept:

Problem: If Inusah's age in 11 years time is three times his age 7 years ago, how old is he now?

Solution:

Let's denote Inusah's current age as x.

7 years ago, he was x - 7 years old.

11 years from now, he will be x 11 years old.

The equation based on the given information is:

3(x - 7) x 11

Now, let's solve the equation step by step:

Simplify the left side: 3x - 21 x 11 Rearrange the equation to isolate x: 3x - x 11 21 2x 32 Divide both sides by 2: x 16

Therefore, Inusah is 16 years old.

Check: 7 years ago, he was 16 - 7 9 years old. 11 years from now, he will be 16 11 27, which is indeed 3 times his age 7 years ago.

Conclusion

Age equations are practical tools that help us solve problems related to time and age. By setting up the right equations and solving them step by step, we can determine the current age of individuals based on future and past conditions. Whether it's a girl's age, your own age, or someone else's age, these equations provide a clear and concise method to arrive at the solution.

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