Select the correct answer.
Molly and Lynn both set aside money weekly for their savings. Molly already has $650 set aside and adds $35 each week. Lynn already has $825 set aside but adds only $15 each week. Which inequality could they use to determine how many weeks, $w$, it will take for Molly's savings to exceed Lynn's savings?
A. $650w+35>825w+15$
B. $650+35w>825+15w$
C. $650w+35<825w+15$
D. $650+35w<825+15w
Answer (1)
Molly's savings after w weeks is 650 + 35 w .
Lynn's savings after w weeks is 825 + 15 w .
The inequality representing when Molly's savings exceed Lynn's savings is 825 + 15w"> 650 + 35 w > 825 + 15 w .
The correct answer is B. 825+15 w"> 650 + 35 w > 825 + 15 w .
Explanation
Problem Analysis Let's analyze the problem. Molly starts with $650 and adds $35 each week. So, after w weeks, Molly's savings will be 650 + 35 w . Lynn starts with $825 and adds $15 each week. So, after w weeks, Lynn's savings will be 825 + 15 w . We want to find the inequality that represents when Molly's savings exceed Lynn's savings. This means we want to find when 825 + 15w"> 650 + 35 w > 825 + 15 w .
Comparing with Options Now, let's compare our inequality with the given options: A. 825w + 15"> 650 w + 35 > 825 w + 15 - This is incorrect because it multiplies the number of weeks, w , by the initial savings and doesn't add the weekly savings correctly. B. 825 + 15w"> 650 + 35 w > 825 + 15 w - This is the correct inequality, as it represents Molly's savings exceeding Lynn's savings. C. 650 w + 35 < 825 w + 15 - This is incorrect for the same reason as option A, and it also has the wrong inequality sign. D. 650 + 35 w < 825 + 15 w - This is incorrect because it represents Molly's savings being less than Lynn's savings.
Conclusion Therefore, the correct inequality is 825 + 15w"> 650 + 35 w > 825 + 15 w .
Examples
Imagine you're saving up for a new video game console that costs $500 . You currently have $200 and save $20 each week. Your friend has $300 and saves $10 each week. The inequality 300 + 10w"> 200 + 20 w > 300 + 10 w helps you determine how many weeks, w , it will take for your savings to exceed your friend's savings, ensuring you get that console first! This type of problem is useful in personal finance to compare savings plans and make informed decisions.
