Directions: Each question below consists of a number. Your task is to follow the following steps in order to find the result from the given alternatives. Step I: Multiply the number by 3 and add the square of the number. Step II: Divide the result obtained after Step I by 5 and add 6. Step III: Divide the result obtained after Step II by 3 and then square the resulting number. 2.5

### Concept & Logic This problem requires following a predefined mathematical algorithm strictly sequentially. When dealing with decimals, converting to fractions often helps maintain precision through intermediate steps. ### Step-by-Step Solution * **Given Input:** $x = 2.5$. It is often easier to use the fraction form $x = \frac{5}{2}$. * **Step I: Multiply the number by 3 and add the square of the number.** $$\text{Result}_1 = 3(2.5) + (2.5)^2$$ $$\text{Result}_1 = 7.5 + 6.25 = 13.75$$ * **Step II: Divide the result obtained after Step I by 5 and add 6.** $$\text{Result}_2 = \frac{13.75}{5} + 6$$ $$\text{Result}_2 = 2.75 + 6 = 8.75$$ * **Step III: Divide the result obtained after Step II by 3 and then square the resulting number.** $$\text{Result}_3 = \left( \frac{8.75}{3} \right)^2$$ Convert $8.75$ to a fraction to make squaring easier: $8.75 = \frac{35}{4}$. $$\text{Result}_3 = \left( \frac{\frac{35}{4}}{3} \right)^2 = \left( \frac{35}{12} \right)^2$$ $$\text{Result}_3 = \frac{1225}{144}$$ Perform the final division: $$1225 \div 144 \approx 8.5069$$ Rounding to two decimal places gives $8.51$. ### Exam Strategy & Shortcut Avoid heavy fraction squaring by using smart decimal estimation at Step 3. $\frac{8.75}{3}$ is slightly less than 3 (since $\frac{9}{3} = 3$). Let's approximate it: $8.75 \div 3 \approx 2.916$. Since $3^2 = 9$, the answer must be slightly less than 9. Looking at the options, 8.10 is too low (that would require $2.84^2$), making 8.51 the only logical approximation. ### Common Pitfall Struggling with the decimal division in Step II ($13.75 \div 5$). A quick trick for dividing any number by 5 is to double the number and divide by 10. $13.75 \times 2 = 27.5$. $27.5 \div 10 = 2.75$. ### Final Answer **Therefore, the correct answer is 8.51 (approx.).**