Question

One third of a number is eight less than the number. What is the number?

Answer 1

Hint: First we need to convert the given word problem into algebraic expression. That is an algebraic expression in mathematics is an expression which is made up of variables and constants along with algebraic operations. An expression is a group of terms. Here algebraic operations are addition, subtraction, division and multiplication etc. After obtaining the algebraic expression we can simplify.

Complete step-by-step answer:
We have One third of a number is eight less than the number
Here we have a number which is unknown and we take it as \[x\].
Now One third of a number means
\[ \Rightarrow \dfrac{1}{3}x\].
Eight less than the number means
\[ \Rightarrow x - 8\]
Then One third of a number is eight less than the number is given by,
\[ \Rightarrow \dfrac{1}{3}x = x - 8\]
Multiply 3 on both sides of the equation,
\[ \Rightarrow x = 3\left( {x - 8} \right)\]
\[ \Rightarrow x = 3x - 24\]
Now we transpose 3x to the left hand side of the equation,
\[ \Rightarrow x - 3x = - 24\]
\[ \Rightarrow - 2x = - 24\]
Divide the whole equation by -2, we have
\[ \Rightarrow x = \dfrac{{ - 24}}{{ - 2}}\]
\[ \Rightarrow x = 12\].
hence the unknown number is 12.
So, the correct answer is “12”.

Note: Algebra helps in converting a mathematical statement into an equation. We know if we have ‘more’ or ‘sum’ in the given sentence we use addition operation\[( + )\]. Similarly If we have ‘less’ or ‘difference’ we use subtraction \[( - )\]. If we have a ‘quotient’ we use division operation \[( \div )\]. To define more generalized terms; we use algebra. It is a very vast branch of mathematics and is used in all the branches of mathematics like polynomial, linear equations, graphs, etc. and in daily life too.