1. **State the problem:** We need to find the value of $x$ given by the formula: $$x=\frac{(3\times14.5)+(5\times24.5)+(8\times34.5)+(10\times44.5)+(12\times54.5)+(7\times64.5)+(3\times74.5)+(2\times84.5)}{3+5+8+10+12+7+3+2}$$ 2. **Formula used:** This is a weighted average formula where the numerator is the sum of products of weights and values, and the denominator is the sum of weights. 3. **Calculate the numerator:** $$3\times14.5=43.5$$ $$5\times24.5=122.5$$ $$8\times34.5=276$$ $$10\times44.5=445$$ $$12\times54.5=654$$ $$7\times64.5=451.5$$ $$3\times74.5=223.5$$ $$2\times84.5=169$$ Sum numerator = $$43.5 + 122.5 + 276 + 445 + 654 + 451.5 + 223.5 + 169 = 2385$$ 4. **Calculate the denominator:** $$3 + 5 + 8 + 10 + 12 + 7 + 3 + 2 = 50$$ 5. **Calculate $x$:** $$x = \frac{2385}{50}$$ 6. **Simplify the fraction:** $$x = \frac{\cancel{2385}^{47.7} \times 50}{\cancel{50}} = 47.7$$ 7. **Final answer:** $$x = 47.7$$ This means the weighted average value is 47.7.