Question

How do you translate into mathematical expressions and find the number given that three less than two – thirds of a number is three?

Answer 1

Hint: In the above problem, we have to convert the given statement into mathematical expression. Let us suppose that the number be x and then the mathematical translation of this statement “three less than two – thirds of a number” is that we have to write $\dfrac{2}{3}$ and multiply with x and then subtract this multiplication from 3 and write it on the one side of the equation and on the other side of the equation we are going to write 3 because in the last line of the statement “is three” is given.

Complete step-by-step solution:
We are going to write the translation of the given statement. For that we are splitting the statement and then write the mathematical expression of the split part and at last will join the parts.
The mathematical expression of the statement “two – thirds of a number” is that we have to multiply $\dfrac{2}{3}$ with x which we have shown as follows:
$\dfrac{2}{3}x$
Now, we are going to write the mathematical expression for the statement “three less than two – thirds of a number” by subtracting 3 from the above multiplication and we get,
$\Rightarrow \dfrac{2}{3}x-3$
In the last part of the statement “three less than two – thirds of a number is three”, it is given that “is three”. This means that we are going to equate the above expression to 3 and we get,
$\Rightarrow \dfrac{2}{3}x-3=3$
In this way, we have written the mathematical translation for the given statement.

Note: In the above problem, the statement contains “three less than two – third of a number” so we have subtracted 3 from $\dfrac{2}{3}x$. Now, suppose if we have given the statement “three more than two – third of a number” then we have to add $\dfrac{2}{3}x$ to 3.