Tanaya (T) is 10 years older than her sister Filita (F) who is 2 years younger than her brother Mario(M). If T, F, M denote their ages, which one of the following represents the given information?
a. $\left{\begin{array}{l}T=F+10 \\ F=M-2\end{array}\right.$
b. $\left{\begin{array}{l}T=F+10 \\ M=F-2\end{array}\right.$
c. $\left{\begin{array}{l}F=T-10 \\ M=F+2\end{array}\right.$
d. $\left{\begin{array}{l}F=T+10 \\ M=F-2\end{array}\right.$
Answer (2)
Express Tanaya's age in terms of Filita's age: T = F + 10 .
Express Filita's age in terms of Mario's age: F = M − 2 .
Combine the equations to represent the relationships.
The correct representation of the given information is: { T = F + 10 F = M − 2
Explanation
Problem Analysis Let's analyze the given information to form equations.
First Equation The first statement is 'Tanaya (T) is 10 years older than her sister Filita (F)'. This can be written as: T = F + 10
Second Equation The second statement is 'Filita (F) is 2 years younger than her brother Mario (M)'. This can be written as: F = M − 2
Finding the Correct Option Now, let's compare our equations with the given options: a. { T = F + 10 F = M − 2 b. { T = F + 10 M = F − 2 c. { F = T − 10 M = F + 2 d. { F = T + 10 M = F − 2 Option a matches our derived equations.
Final Answer Therefore, the correct answer is option a.
Examples
Understanding relationships between ages can help in various real-life scenarios, such as planning family events or understanding demographic trends. For example, if you know the age difference between family members, you can predict their ages in the future or analyze age distributions in a population to understand dependency ratios and plan social services.
The correct representation of the relationships given in the problem is option a: { T = F + 10 F = M − 2 This states that Tanaya is 10 years older than Filita, and Filita is 2 years younger than Mario. These equations accurately reflect the information provided in the question.
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