Question

A package of $25$ mechanical pencils cost $\$ 5.75$. How much does each pencil cost?

Answer 1

Hint: Here in this question, we have to find the cost of a single mechanical pencil by using the data. This can be solved by firstly, we have to take the cost of each pencil as x. later isolate x by using the basic arithmetic operation like addition, subtraction, multiplication and division on simplification we get the required solution.

Complete step-by-step solution:
In mathematics we have four different kinds of arithmetic operations namely
Addition, which adds the numbers and the sign for the addition is +
Subtraction, which subtracts the numbers and the sign for the subtraction is –
Multiplication, which multiplies the numbers and the sign for the multiplication is \[ \times \]
Division, which divides the numbers and the sign for the division is \[ \div \]
First, we will start off by evaluating the given condition which is, the cost of $25$ mechanical pencils is $\$ 5.75$.
Here we have to find the cost of a single mechanical pencil.
Now, let us consider the price of one or single pencil as $x$.
So, according to the condition we can written the cost of 25 mechanical pencil as:
$ \Rightarrow \,\,\,25x = \$ 5.75$
Now we will take all the variable terms to one side and all the integer terms to another side by dividing both side by 25 Hence, the equation will become,
$ \Rightarrow x = \dfrac{{\$ 5.75}}{{25}}$
Now, we will solve for the value of $x$ by evaluating or simplified the value of the fraction, we get
$ \Rightarrow \,\,\,x = \$ 0.23$

Therefore, the price of one or each mechanical pencil is $\$ 0.23$.

Note: While using the arithmetic operations we must know about the numbers and the tables of multiplication. This is a word problem, where the word problem is converted into the numeral form. The arithmetic operations are used whenever it is needed and then we have to simplify.