Question

One-fifth of a number minus $$4$$ gives $$3$$.

Answer 1

Hint: Here, we will assume the required number to be some variable. We will first find the one fifth of the number and then subtract 4 from it and then equate it to 3 to get a linear equation. We will solve the equation further to get the required answer. A linear equation is an equation which has the highest degree of 1 and has only one solution.

Complete step-by-step solution:
Let the unknown number be $$x$$.
According to the question, one fifth of $$x$$ minus four gives three.
This means that we first have to take the one fifth of the unknown number, which in turn means that we have to multiply it by $${\displaystyle \frac{1}{5}}$$ or divide by $$5$$.
On dividing $$x$$ by five, we get $${\displaystyle \frac{x}{5}}$$.
Now, four has to be subtracted from the one fifth of the unknown number. On subtracting four from $${\displaystyle \frac{x}{5}}$$, we get $$\left({\displaystyle \frac{x}{5}}-4\right)$$.
We will now equate the above expression to 3, so that we can write the mathematical equation as:
$${\displaystyle \frac{x}{5}}-4=3$$
Adding $$4$$ on both the sides, we get
$$\Rightarrow {\displaystyle \frac{x}{5}}=7$$
On multiplying both the sides by $$5$$, we get
$$\Rightarrow x=35$$

Therefore, the value of the required number is 35.

Note:
While converting a statement into a mathematical expression, we have to take proper care of the BODMAS rule. We might misinterpret the given statement as one-fifth of the number obtained by subtracting four from the unknown number is equal to three, and generate the mathematical equation as $${\displaystyle \frac{x-4}{5}}=3$$. Here comes the significance of the BODMAS rule according to which the division must be performed before the subtraction, and hence the equation is $${\displaystyle \frac{x}{5}}-4=3$$.