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If $$2\frac{1}{2}$$ is added tp a number and the sum multiplied by $$4\frac{1}{2}$$ and 3 is added to the product and the sum is divided by $$1\frac{1}{5}$$, the quotient becomes 25. What is the number ?

If $$2\frac{1}{2}$$ is added tp a number and the sum multiplied by $$4\frac{1}{2}$$ and 3 is added to the product and the sum is divided by $$1\frac{1}{5}$$, the quotient becomes 25. What is the number ? Correct Answer $$3\frac{1}{2}$$

Let the number be x
Then,
$$\eqalign{ & \Leftrightarrow \frac{{4\frac{1}{2}\left( {x + 2\frac{1}{2}} \right) + 3}}{{1\frac{1}{5}}} = 25 \cr & \Leftrightarrow \frac{{\frac{9}{2}\left( {x + \frac{5}{2}} \right) + 3}}{{\frac{6}{5}}} = 25 \cr & \Leftrightarrow \frac{{9x}}{2} + \frac{{45}}{4} + 3 = 25 \times \frac{6}{5} \cr & \Leftrightarrow \frac{{9x}}{2} + \frac{{45}}{4} + 3 = 30 \cr & \Leftrightarrow \frac{{9x}}{2} = 30 - \frac{{57}}{4} \cr & \Leftrightarrow \frac{{9x}}{2} = \frac{{63}}{4} \cr & \Leftrightarrow x = \left( {\frac{{63}}{4} \times \frac{2}{9}} \right) \cr & \Leftrightarrow x = \frac{7}{2} \cr & \Leftrightarrow x = 3\frac{1}{2} \cr} $$

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