One fourth of a number is increased by 7 and the result is multiplied by 3. Thus, we obtain 36. Find the number.

Let the required number be x.

One-fourth of the number increased by 7 is $\Big(\dfrac{x}{4} + 7\Big)$.

According to the given condition we have:

$\phantom{=} 3 \times \Big(\dfrac{x}{4} + 7\Big) = 36 \\[1em] \Rightarrow \dfrac{x}{4} + 7 = \dfrac{36}{3} \\[1em] \Rightarrow \dfrac{x}{4} + 7 = 12 \\[1em] \Rightarrow \dfrac{x}{4} = 12 - 7 \quad \text{[Transposing +7 to RHS]} \\[1em] \Rightarrow \dfrac{x}{4} = 5 \\[1em] \Rightarrow x = 5 \times 4 \\[1em] \Rightarrow x = 20$

Hence, the required number is 20.