Find a number whose double is 45 greater than its half.

Let the number be $\mathrm{x}$.

According to the question,

$2 \mathrm{x}=\frac{1}{2} \mathrm{x}+45$

or $2 \mathrm{x}-\frac{1}{2} \mathrm{x}=45$

or $\frac{4 \mathrm{x}-\mathrm{x}}{2}=45$

or $3 \mathrm{x}=90[$ After c ross multiplication $]$

or $\mathrm{x}=\frac{90}{3}$

or $\mathrm{x}=30$

Thus, the number is 30 .