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?
J - S = 2; S + J = 26.
This system of equations correctly represents the relationship between Samantha's age and Jake's age. The first equation, J - S = 2, reflects that Samantha is 2 years younger than Jake, while the second equation, S + J = 26, captures the total of their ages.
This choice accurately models the situation described in the problem. The first equation indicates that Jake is 2 years older than Samantha, and the second equation states that their combined ages total 26 years. Hence, this system can be used to find both of their ages.
This choice incorrectly implies that Samantha's age minus 2 equals Jake's age, which suggests that Samantha is older than Jake. This contradicts the information provided in the problem, where Samantha is younger than Jake. Therefore, this system cannot correctly represent their ages.
This choice has multiple issues: it incorrectly uses lowercase 'j' instead of uppercase 'J', and it states S - j = 2, which implies that Samantha is older than Jake. Additionally, the total age equation incorrectly sums their ages to 24 instead of 26, making this an incorrect representation of the problem.
This choice incorrectly suggests that both Samantha and Jake are equal to 2 years old, which is not only incorrect but also does not solve the problem as it misrepresents their age relationship and the total of their ages.
The correct representation of Samantha and Jake's ages is given by the equations J - S = 2 and S + J = 26. This system effectively captures the relationship between their ages and their total age, allowing for the correct calculation of both individuals' ages. The other options fail to accurately reflect the conditions of the problem and thus cannot be used to derive a solution.
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