Stuck in a simple maths question where I need to find the value of variable $a$

Question

Let's assume

$$a = 423,$$

and now we need to calculate the variable $b$, given the fact that when $5\%$ of variable $b$ is added to it, it gives the value of $a$.

$$a = b + \frac{5\cdot b}{100}.$$

Calculate the value of $b$.

Answer 1

$$423 = b\Bigl(1+\frac{5}{100}\Bigr)$$

$$423 = \frac{105b}{100}$$

$$423 = \frac{21b}{20}$$

$$\frac{423•20}{21} = b$$

$$b = \frac{3•141•20}{3•7} = \frac{2820}{7}$$

Hope this helped.

Answer 2

$a=b(1)+b(5/100)=b(1+5/100)=b(1.05).$ Therefore $b=b(1.05)/1.05=a/1.05.$

Answer 3

$$423=\frac{105b}{100}\implies42300=105b\implies b=\frac{42300}{105}$$

Now just reduce and you have your answer.