5. Bao is considering getting a part-time job. Instead of taking money out of his account each month, he would put money in. His account still has \( \$ 175 \), and his goal is to have at least \( \$ 1,000 \) in the account a year from now. a Write an inequality where \( x \) represents the amount of money Bao should put in each month to reach his goal. b Solve the inequality you wrote and explain what the solutions mean in Bao's situation.

Let's help Bao determine how much he needs to save each month to reach his financial goal. We'll break this down into two parts: ### **a) Writing the Inequality** **Given:** - **Current Savings:** \$175 - **Goal after 1 Year:** At least \$1,000 - **Time Frame:** 12 months - **Monthly Savings:** Let \( x \) represent the amount Bao saves each month. **Objective:** Find the inequality that represents the situation. **Steps:** 1. **Total Savings from Monthly Deposits:** If Bao saves \( x \) dollars each month for 12 months, he will save a total of \( 12x \) dollars in a year. 2. **Total Account Balance After 1 Year:** This will be his current savings plus the total from his monthly deposits: \[ \text{Total} = 175 + 12x \] 3. **Setting Up the Inequality:** Bao wants this total to be **at least** \$1,000. Therefore: \[ 175 + 12x \geq 1,\!000 \] **Inequality:** \[ 175 + 12x \geq 1,\!000 \] --- ### **b) Solving the Inequality and Interpretation** **Inequality to Solve:** \[ 175 + 12x \geq 1,\!000 \] **Steps to Solve:** 1. **Subtract 175 from Both Sides:** \[ 12x \geq 1,\!000 - 175 \] \[ 12x \geq 825 \] 2. **Divide Both Sides by 12 to Solve for \( x \):** \[ x \geq \frac{825}{12} \] \[ x \geq 68.75 \] **Solution:** \[ x \geq \$68.75 \] **Interpretation:** - **Minimum Monthly Savings:** Bao needs to save **at least \$68.75 each month** to reach his goal of having \$1,000 in his account after one year. - **Practical Consideration:** Since saving exactly \$68.75 might be cumbersome, Bao could opt to save **\$69 per month** to ensure he meets or slightly exceeds his goal. **Summary:** By committing to saving \$69 each month, Bao will ensure that his savings grow from his current \$175 to meet or exceed his target of \$1,000 within a year.