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Cole's age is 3 years less than his sister Tina's age, \( t \). If Cole is 18 , which equation represents this situation, and how old is Tina? A. The equation that represents this situation is \( t-3=18 \). Tina is 21 . B. The equation that represents this situation is \( t+3=18 \). Tina is 15 . C. The equation that represents this situation is \( 3-t=18 \). Tina is 21 . D. The equation that represents this situation is \( -3-t=18 \). Tina is 15 .

Ask by Alexander Gibson. in the United States
Mar 09,2025

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Tutor-Verified Answer

Answer

The equation is \( t - 3 = 18 \), and Tina is 21 years old.

Solution

1. Write the relationship: Cole's age is 3 years less than Tina's age. Since \( t \) represents Tina's age, we have \[ t - 3 = 18. \] 2. Solve for \( t \): \[ \begin{aligned} t - 3 &= 18 \\ t &= 18 + 3 \\ t &= 21. \end{aligned} \] 3. Therefore, the equation representing the situation is \[ t - 3 = 18, \] and Tina is 21 years old. The correct answer is A.

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The Deep Dive

To figure out the equation representing the situation, let's unpack the information given. Since Cole's age is 3 years less than Tina's age, we can write this relationship as \( t - 3 = 18 \). When we solve for \( t \), we add 3 to both sides, resulting in \( t = 21 \). So, the correct answer is A: The equation is \( t - 3 = 18 \) and Tina is indeed 21. Now, looking at how age relationships work, it’s important to remember that these kinds of word problems can often be translated into algebraic equations. The key is to identify the relationships first, just like how we found that Cole is younger than Tina. This way, you can set up the equations correctly and solve them without getting tangled in unnecessary confusion!

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