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Comprehensive Guide to Solving the Age Problem Involving Brad and Shantel

Introduction:

We are faced with a classic age problem. We know two things: the sum of Brad and Shantel’s current ages is 83, and 9 years ago, Brad’s age was four times Shantel’s age. Our mission is to determine their current ages using this information.

Step 1: Define the Variables

First, let’s assign variables to unknown quantities. We’ll use B to represent Brad’s current age and S for Shantel’s current age. These variables will help us formulate equations based on the given conditions.

Step 2: Translate the Problem into Mathematical Equations

1. The first piece of information tells us that the sum of their current ages is 83. Mathematically, this can be expressed as B + S = 83.

2. The second piece of information is a bit more complex. It tells us that 9 years ago, Brad’s age was four times Shantel’s age. To represent their ages 9 years ago, we subtract 9 from their current ages. Brad’s age 9 years ago becomes B – 9, and Shantel’s becomes S – 9. This condition can be translated into the equation: B – 9 = 4(S – 9).

Step 3: Simplify and Rearrange the Second Equation

Now, let’s work on simplifying the second equation. Expanding the terms inside the parentheses, we get B – 9 = 4S – 36. Further rearranging gives us B – 4S = -27.

Step 4: Solve the Equations Simultaneously

We have two equations to solve:

1. B + S = 83 (This equation represents the sum of their current ages)

2. B – 4S = -27 (This equation represents the age condition 9 years ago)

We’ll add the two equations together to eliminate the variable S. Doing so, we get 2B – 3S = 56. Solving for B in terms of S, we find B = 28 + 3/2S.

Next, we’ll substitute this value into the first equation (B + S = 83) to find S. Solving the resulting equation, we find S = 22.

Finally, we’ll substitute this value of S back into the first equation (B + S = 83) to find B. Doing so, we find B = 61.

Conclusion:

After solving the equations, we find that Brad is currently 61 years old, and Shantel is currently 22 years old.