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.

A)1000 - 100w ≤ 500; w ≥ 6
B)1000 + 100w ≤ 500; w ≤ 5
C)1000 + 100w ≥ 500; w ≥ 6
D)1000 - 100w ≥ 500; w ≤ 5

Answer 1

D) 1000 - 100w ≥ 500; w ≤ 5

Explanation:

The correct answer is 1000 - 100w ≥ 500; w ≤ 5. Take the starting amount, 1000, and subtract 100 “w” times (“w” is the number of weeks). This expression must be ≥ 500 since she wants to have at least $500. Solve the inequality to get the answer.

Answer 2

ANSWER:
D) 1000 - 100w
`\geq` 500; w
`\leq` 5

WHY NOT A?
Well, choice a says that you can have less than or equal to $500 (
`\leq 500`), but she wants $500 or more. Additionally, she can only do it for 5 weeks, but the equation says 6 weeks (w
`\geq 6`).

WHY NOT B?
This choice says that she will be adding $100 a week (+100w), when the problem states, "She withdraws $100 a week".

WHY NOT C?
This choice says that she will be adding $100 a week (+100w), when the problem states, "She withdraws $100 a week". Also, this question says that she will do it for 6 weeks when she can only do it for 5 weeks or less.