Samantha is 2 years younger than Jake. The total of their ages is 26. What are the ages of Samantha and Jake? Let S be Samantha's age and let J be Jake's age. Which of the following systems of equations can be used to solve the word problem shown?

Rationale

Samantha's age can be represented as S = J - 2.

This equation accurately reflects the relationship that Samantha is 2 years younger than Jake. By rearranging this expression, we can isolate Samantha's age in terms of Jake's age, facilitating the solution of the problem alongside the total age equation.

A (J - S = 2, S + J = 26) YOUR ANSWER

This equation expresses that Jake is 2 years older than Samantha, which is the opposite of the given relationship where Samantha is younger. Therefore, this representation is incorrect based on the problem's conditions.

B (S - 2 = J, S + J = 26) YOUR ANSWER

This equation implies that if you subtract 2 from Samantha's age, you obtain Jake's age. However, this does not align with the problem's description; rather, it suggests that Samantha is older than Jake, which contradicts the information provided.

C (S - J = 2, S + J = 26) YOUR ANSWER

This equation indicates that Samantha is 2 years older than Jake, which is again the opposite of the correct relationship stated in the problem. Thus, it fails to represent the correct ages of Samantha and Jake.

D (S = J - 2, S + J = 26) CORRECT

This equation correctly shows that Samantha's age is 2 years less than Jake's age, aligning perfectly with the problem statement. It accurately captures the relationship between their ages and can be used effectively in conjunction with the total age equation.

Conclusion

The correct system of equations to model the ages of Samantha and Jake is represented by option D. This accurately reflects the relationship that Samantha is 2 years younger than Jake, while also allowing for the total age equation to be included. The other options misrepresent the relationship, leading to incorrect interpretations of their ages.

Samantha is 2 years younger than Jake. The total of their ages is 26. What are the ages of Samantha and Jake? Let S be Samantha's age and let J be Jake's age. Which of the following systems of equations can be used to solve the word problem shown?

Samantha's age can be represented as S = J - 2.

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