Amy has $1,000 in a savings account at the beginning of the fall. She wants to have at least $500 in the account by the end of the fall. She withdraws $100 a week for living expenses. Write an inequality for the number of weeks Amy can withdraw money, and solve.

Question

Amy has $1,000 in a savings account at the beginning of the fall. She wants to have at least $500 in the account by the end of the fall. She withdraws $100 a week for living expenses. Write an inequality for the number of weeks Amy can withdraw money, and solve.

Answer 1

Let's start by defining the variables:

Let w be the number of weeks Amy can withdraw money.

Amy's weekly withdrawals will reduce her account balance by $100 for each week. Therefore, the amount of money left in her account after w weeks will be 1000 - 100w.

According to the problem, Amy wants to have at least $500 in the account by the end of the fall. Therefore the inequality is:
1000 - 100w ≥ 500

Now we can solve for w:
1000 - 100w ≥ 500
1000 - 500 ≥ 100w
500 ≥ 100w
Dividing both sides of the inequality by 100 we get:
5 ≥ w

Therefore, the number of weeks Amy can withdraw money is at most 5.