Question

lilys bank account has a balance of $620. she withdraws $80 once to pay for her dogs visit to the veterinarian. then she withdraws $45 every week to pay the dog sitter. lily does not make any other withdrawals from this account, and she does not deposit any money into it. determine the range of weeks when lily will have more than $90 in the account. write and solve an inequality to model the situation. ph the solution set of the inequality on the number line. ine the range of the number of weeks. consider restrictions to the solution set based ontext. explain your thinking.

Explanation:

Step1: Define variables and form inequality

Let \( w \) be the number of weeks. Initial balance is $620, withdraw $80 once, then $45 per week. The amount left is LXI1, which should be more than $90. So inequality: \( 620 - 80 - 45w > 90 \).

Step2: Simplify left side

Calculate \( 620 - 80 = 540 \), so inequality becomes \( 540 - 45w > 90 \).

Step3: Subtract 540 from both sides

\( -45w > 90 - 540 \), which is \( -45w > -450 \).

Step4: Divide by -45 (reverse inequality)

Dividing both sides by -45 (inequality sign flips): \( w < 10 \). Since weeks can't be negative, \( 0 \leq w < 10 \) (but \( w \) is positive integer in context, so \( w = 0,1,...,9 \)).

Answer:

The inequality is \( 620 - 80 - 45w > 90 \) (or simplified \( 540 - 45w > 90 \)), and the solution is \( w < 10 \) (with \( w \) representing weeks, so \( 0 \leq w < 10 \) in context).