8. 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: A
Samantha and Jake's ages can be represented by the equations J - S = 2 and S + J = 26.
The system of equations that correctly represents the relationship between Samantha's and Jake's ages is J - S = 2 and S + J = 26.
A) J - S = 2; S + J = 26
This option is correct as it accurately reflects the information provided in the problem. The first equation, J - S = 2, indicates that Jake is 2 years older than Samantha, while the second equation, S + J = 26, states that their combined ages total 26.
B) S - 2 = J; S + J = 26
This option incorrectly states the relationship between their ages. It suggests that Samantha is 2 years older than Jake, which contradicts the given information that Samantha is younger.
C) S - j = 2; S + j = 24
This option is incorrect as it misrepresents both the age difference and the total sum of their ages. The equation S - j = 2 implies that Samantha is older than Jake by 2 years, and the total age of 24 is also incorrect since the problem states their ages sum to 26.
D) S = j = 2; S + j = 24
This option is incorrect as it incorrectly states that both Samantha and Jake are 2 years old and sums their ages to 24, which does not align with the conditions of the problem. The equality S = j = 2 fails to represent the relationship described in the problem.
Conclusion
Option A is definitively correct as it accurately captures the age relationship and total age of Samantha and Jake as described in the problem. All other options either misstate the relationship or provide incorrect totals, making them invalid for solving the given word problem.