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 \[\dfrac{1}{5}\] or divide by \[5\].
On dividing \[x\] by five, we get \[\dfrac{x}{5}\].
Now, four has to be subtracted from the one fifth of the unknown number. On subtracting four from \[\dfrac{x}{5}\], we get \[\left( {\dfrac{x}{5} - 4} \right)\].
We will now equate the above expression to 3, so that we can write the mathematical equation as:
\[\dfrac{x}{5} - 4 = 3\]
Adding \[4\] on both the sides, we get
\[ \Rightarrow \dfrac{x}{5} = 7\]
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 \[\dfrac{{x - 4}}{5} = 3\]. Here comes the significance of the BODMAS rule according to which the division must be performed before the subtraction, and hence the equation is \[\dfrac{x}{5} - 4 = 3\].