Question

Jacob has $1,000 in a checking account and withdraws $40 each week. His account requires a minimum balance of more than $400. Write an inequality to model the number of weeks, x, that he can withdraw $40 to maintain the minimum balance requirement.

A.
x > 15
B.
x < 18
C.
x ≤ 18
D.
x < 15

Answer 1

To determine how many weeks Jacob can withdraw $40 while keeping his balance above $400, we start by calculating his account balance after \( x \) weeks.

Jacob starts with $1,000 and withdraws $40 each week. Therefore, after \( x \) weeks, his balance will be:

\[
1000 - 40x
\]

We need to ensure that this balance remains greater than $400 since the account requires a minimum balance of more than $400. This can be expressed as the inequality:

\[
1000 - 40x > 400
\]

Now, we can solve this inequality:

1. Subtract 1000 from both sides:

\[
-40x > 400 - 1000
\]
\[
-40x > -600
\]

2. Divide both sides by -40. Remember, when dividing or multiplying by a negative number, the inequality sign flips.

\[
x < \frac{-600}{-40}
\]
\[
x < 15
\]

Therefore, the inequality that models the number of weeks \( x \) that Jacob can withdraw $40, while maintaining the minimum balance requirement, is:

\[
x < 15
\]

The correct answer is:

**D. x < 15**