Question

What is the equation that expresses one half of a certain number n is 95?

Answer 1

Hint: The easiest way to write an algebraic equation from a sentence is to first break it into parts as per the left hand side, and the right hand side. Then, we must look for the unknown quantity, and assume it to be a variable (say $$n$$). And then, we must perform suitable operations, as needed.

Complete step by step solution:
The verbal representation of the required algebraic equation is “one half of a certain number n is 95.” Here, we do not have any information regarding the “certain number” mentioned in our above statement.
So, we are assuming this “certain number” to be $$n$$ as given in the question.
Now, we will proceed by observing what operations are performed on this “certain number”.
The first part of our statement says “one half of a certain number”.
We know that the phrase ‘one half’ denotes a multiplication by ${\displaystyle \frac{1}{2}}$ or a division by 2, that is, the number $$n$$ is divided by 2.
And so, our expression now becomes $$\left({\displaystyle \frac{n}{2}}\right)$$.
Now, let us now include the remaining part of the given sentence. We now have the sentence, “one half of a certain number n is 95”.
So, now by using our past steps, we can also write this statement as “ $$\left({\displaystyle \frac{n}{2}}\right)$$ is 95”.
So, our required equation now evaluates to $$\left({\displaystyle \frac{n}{2}}\right)=95$$.

Hence, our required algebraic equation is $${\displaystyle \frac{n}{2}}=95$$.

Note: We must read, very carefully, that on which part of our expression, any specified operation is taking place. We must keep in mind that the words and phrases such as “is, is equal to, matches” represents the equality sign.