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?

Rationale

Person A and Person B will have the same amount of money after 5 weeks.

This is calculated by finding out the difference in their initial amounts and the rate at which they save per week. Person A starts with $60 and saves $10 weekly, while Person B starts with $50 and saves $15 weekly. The difference in their initial amounts is $10, and the difference in their saving rates is $5 per week. Therefore, it will take 2 weeks (10/5) for Person B to catch up to the initial amount of Person A, and they will have the same amount of money from the 5th week onward.

A (2 weeks) CORRECT

This choice correct assumes that the two people will have the same amount of money after 2 weeks. Person B's saving rate is higher than Person A's by $5 per week. Thus, the initial $10 difference between their amounts will be eliminated after 2 weeks, after which Person B will start to catch up.

B (2.7 weeks) YOUR ANSWER

This choice incorrectly assumes a fractional week, which is not possible in this context. Savings occur on a weekly basis, so it is not valid to consider fractions of a week.

C (10 weeks) YOUR ANSWER

This choice incorrectly assumes that it will take 10 weeks for Person B to catch up to Person A. However, given that Person B is saving at a faster rate than Person A, they will have the same amount of money much earlier than 10 weeks.

D (5 weeks) YOUR ANSWER

This is incorrect answer. After 2 weeks, Person B will have caught up to the initial amount of Person A.

Conclusion

The question requires determining when Person A and Person B will have the same amount of money given their different initial amounts and different saving rates. By calculating the time it takes for Person B to make up the initial difference and then considering the weekly savings rate, we can conclude that they will both have the same amount of money after 2 weeks.

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?

Person A and Person B will have the same amount of money after 5 weeks.

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