Adele is 5 years older than Timothy. In three years, Timothy will be $\frac{2}{3}$ of Adele's age. What is Adele's current age?
Answer (2)
Define Adele's age as A and Timothy's age as T , establishing the equation A = T + 5 .
Express the relationship in three years as T + 3 = 3 2 ( A + 3 ) .
Substitute A in the second equation to solve for T , finding T = 7 .
Calculate Adele's age using A = T + 5 , resulting in A = 12 . The final answer is 12 .
Explanation
Problem Analysis Let's analyze the problem. We are given that Adele is 5 years older than Timothy. We are also given that in three years, Timothy's age will be 3 2 of Adele's age. We need to find Adele's current age.
Defining Variables and First Equation Let A be Adele's current age and T be Timothy's current age. From the first statement, we have: A = T + 5
Second Equation In three years, Adele's age will be A + 3 and Timothy's age will be T + 3. From the second statement, we have: T + 3 = 3 2 ( A + 3 )
Substitution Substitute A = T + 5 into the second equation: T + 3 = 3 2 ( T + 5 + 3 ) T + 3 = 3 2 ( T + 8 )
Eliminating the Fraction Multiply both sides by 3 to eliminate the fraction: 3 ( T + 3 ) = 2 ( T + 8 ) 3 T + 9 = 2 T + 16
Solving for Timothy's Age Solve for T: 3 T − 2 T = 16 − 9 T = 7
Solving for Adele's Age Substitute the value of T back into A = T + 5 to find A: A = 7 + 5 A = 12
Final Answer Therefore, Adele's current age is 12 years.
Examples
Understanding age-related problems can be useful in various real-life situations, such as planning for retirement, calculating insurance premiums, or even in genetics to understand inheritance patterns. For example, if you know the age difference between family members and a future age relationship, you can determine their current ages, which can be helpful in family planning or understanding genealogical data. The problem we solved uses basic algebra to relate the ages of two people at different points in time, which is a fundamental skill in quantitative reasoning.
Adele is currently 12 years old. This was determined by establishing a relationship between her age and Timothy's age and solving the equations formed from the given conditions.
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