2. Person A has $60, and Person B has $50. Person A is saving $10 per week, and Person B is saving $15 per week. How many weeks do they need to save before they have the same amount of money?
Answer: A
Person A and Person B will have the same amount of money in 2 weeks.
After 2 weeks of saving, both Person A and Person B will have equal amounts of money. Person A's savings will increase by $20 ($10 per week for 2 weeks), totaling $80, while Person B's savings will increase by $30 ($15 per week for 2 weeks), totaling $80 as well.
A) 2 weeks
This option is correct because after 2 weeks, Person A will have $80 ($60 + $20) and Person B will also have $80 ($50 + $30). Thus, they will have the same amount of money.
B) 2.7 weeks
This option is incorrect because it suggests a fractional week, which is not applicable in this context. The calculations for both individuals do not yield an equal amount until the full 2 weeks are completed.
C) 10 weeks
This option is incorrect as it significantly overestimates the time needed for both individuals to reach the same amount. In 10 weeks, Person A would have $160, and Person B would have $200, which does not result in equal amounts.
D) 5 weeks
This option is incorrect because, at 5 weeks, Person A would have $110 ($60 + $50) and Person B would have $125 ($50 + $75), which means they still would not have the same amount of money.
Conclusion
In conclusion, the correct answer is 2 weeks, as this is the only option where the amounts for both Person A and Person B equalize based on their initial savings and weekly contributions. All other options fail to provide a valid solution, either by underestimating or overestimating the required time to achieve equal amounts.