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1. 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 ?

A. $2 \frac{1}{2}$

B. $3 \frac{1}{2}$

C. $4 \frac{1}{2}$

D. $5 \frac{1}{2}$

Solution:

Let the number be x
Then,

\begin{aligned} \Leftrightarrow \frac{4 \frac{1}{2} (x + 2 \frac{1}{2}) + 3}{1 \frac{1}{5}} = 25 \\ \Leftrightarrow \frac{\frac{9}{2} (x + \frac{5}{2}) + 3}{\frac{6}{5}} = 25 \\ \Leftrightarrow \frac{9 x}{2} + \frac{45}{4} + 3 = 25 \times \frac{6}{5} \\ \Leftrightarrow \frac{9 x}{2} + \frac{45}{4} + 3 = 30 \\ \Leftrightarrow \frac{9 x}{2} = 30 - \frac{57}{4} \\ \Leftrightarrow \frac{9 x}{2} = \frac{63}{4} \\ \Leftrightarrow x = (\frac{63}{4} \times \frac{2}{9}) \\ \Leftrightarrow x = \frac{7}{2} \\ \Leftrightarrow x = 3 \frac{1}{2} \end{aligned}

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