1. **Problem Statement:** (a) Calculate the final balance of the Home Science Club for March 2023 after a series of earnings and spendings starting with Nu. 200. (b) Solve and analyze the inequality $x^2 - 6x + 8 > 0$ and sketch its rough graph. --- 2. **Part (a) - Calculating Final Balance:** - Initial balance = Nu. 200 - On 4th day, earned Nu. 5300: New balance = $200 + 5300 = 5500$ - On 7th day, spent Nu. 3150: New balance = $5500 - 3150 = 2350$ - On 8th day, earned Nu. 6600: New balance = $2350 + 6600 = 8950$ - On 12th day, spent Nu. 4100: New balance = $8950 - 4100 = 4850$ - After 5 days (17th), earned Nu. 8850: New balance = $4850 + 8850 = 13700$ - On 23rd day, spent Nu. 4125: New balance = $13700 - 4125 = 9575$ - On 24th day, earned Nu. 9990: New balance = $9575 + 9990 = 19565$ **Final balance at the end of March = Nu. 19565** --- 3. **Part (b) - Solving the inequality $x^2 - 6x + 8 > 0$:** - First, factorize the quadratic: $$x^2 - 6x + 8 = (x - 2)(x - 4)$$ - The roots are $x = 2$ and $x = 4$. - The parabola opens upwards (coefficient of $x^2$ is positive). - The inequality $x^2 - 6x + 8 > 0$ means the quadratic is positive. - This happens when $x < 2$ or $x > 4$. - Between the roots $2 < x < 4$, the quadratic is negative. --- 4. **Graphical Interpretation:** - The parabola crosses the x-axis at $x=2$ and $x=4$. - Above the x-axis (positive) for $x < 2$ and $x > 4$. - Below the x-axis (negative) for $2 < x < 4$. --- **Final answers:** - (a) Final balance = Nu. 19565 - (b) Solution to inequality: $x < 2$ or $x > 4$