Answer:
D. ![1000 - 100w \geq 500; w \leq 5](https://tex.z-dn.net/?f=1000%20-%20100w%20%5Cgeq%20500%3B%20w%20%5Cleq%205)
Step-by-step explanation:
Given:
Initial amount in the bank = $1000
Money withdrawn each week = $100
Final amount should be at least $500.
Now, let the number of weeks the money is withdrawn be 'w'.
Therefore,
Money withdrawn in 'w' weeks = ![\textrm{Money withdrawn each week}\times w](https://tex.z-dn.net/?f=%5Ctextrm%7BMoney%20withdrawn%20each%20week%7D%5Ctimes%20w)
Total Money withdrawn in 'w' weeks = ![100w](https://tex.z-dn.net/?f=100w)
Now, final amount after 'w' weeks is equal to the difference between initial amount and total withdrawal amount. Therefore,
Final amount = Initial amount - Total withdrawal amount
Final amount = ![1000 - 100w](https://tex.z-dn.net/?f=1000%20-%20100w)
Now, final amount must be greater than or equal to $500. So,
![\textrm{Final amount}\geq500\\\\1000-100w\geq500](https://tex.z-dn.net/?f=%5Ctextrm%7BFinal%20amount%7D%5Cgeq500%5C%5C%5C%5C1000-100w%5Cgeq500)
Therefore, the inequality that represents the inequality for the number of weeks Amy can withdraw money is:
![1000-100w\geq500](https://tex.z-dn.net/?f=1000-100w%5Cgeq500)
Now, let us solve for 'w'.
Adding -500 and 100w both sides, we get:
![1000-500-100w+100w\geq500-500+100w\\\\500\geq100w\\\\\textrm{The above inequality is reversed when taking 100w on the left side}\\\\100w\leq500\\\\w\leq\frac{500}{100}\\\\\therefore w\leq5](https://tex.z-dn.net/?f=1000-500-100w%2B100w%5Cgeq500-500%2B100w%5C%5C%5C%5C500%5Cgeq100w%5C%5C%5C%5C%5Ctextrm%7BThe%20above%20inequality%20is%20reversed%20when%20taking%20100w%20on%20the%20left%20side%7D%5C%5C%5C%5C100w%5Cleq500%5C%5C%5C%5Cw%5Cleq%5Cfrac%7B500%7D%7B100%7D%5C%5C%5C%5C%5Ctherefore%20w%5Cleq5)
Therefore, the correct option is (D).