10. 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?
Answer: D
Samantha is 2 years younger than Jake, and their combined ages total 26.
To express that Samantha is 2 years younger than Jake, we can write the equation S = J - 2. Additionally, since their ages total 26, we use the equation S + J = 26. Thus, the system of equations represented by these statements is accurately captured by option D.
A) J - S = 2, S + J = 26
This option incorrectly states that Jake is 2 years older than Samantha, as indicated by the equation J - S = 2. The problem specifies that Samantha is younger than Jake, making this option incorrect.
B) S - 2 = J, S + J = 26
While this option includes the correct total of their ages, the first equation incorrectly suggests that Samantha is 2 years older than Jake, which contradicts the information given in the problem.
C) S - J = 2, S + J = 26
This option also misrepresents the relationship between Samantha and Jake's ages by stating that Samantha is 2 years older than Jake, indicated by the equation S - J = 2. Therefore, this option is not valid.
D) S = J - 2, S + J = 26
This option accurately reflects the relationship that Samantha is 2 years younger than Jake with the equation S = J - 2. It also correctly states that their combined ages total 26 with S + J = 26, making it the correct choice.
Conclusion
Option D is definitively correct as it properly captures both the age difference and the total age of Samantha and Jake. The other options either misinterpret the relationship between their ages or provide incorrect equations, failing to align with the context of the problem.