Question

John’s age increased by $ 11 $ is $ 5 $ less than $ 5 $ times his age. How old is he?

Answer 1

Hint: Here we are not given the age of John so will assume that his age be denoted by “x” and then will frame the given word statements in the form of the mathematical expressions and then will simplify for the required solutions.

Complete step by step solution:
Let us assume that John’s age be denoted by “x”
Frame the equation by using the statement: John’s age increased by $ 11 $ is $ 5 $ less than $ 5 $ times his age.
 $ \Rightarrow x + 11 = 5x - 5 $
The above equation can be re-written as –
 $ \Rightarrow 5x - 5 = x + 11 $
Take all like terms on one side of the equation. The term with “x” on the left hand side and the constants on the right hand side of the equation. When you move any term from one side of the equation to the opposite side then the sign of the terms also changes. Positive terms become negative and the negative term becomes positive.
 $ \Rightarrow 5x - x = 11 + 5 $
Simplify the above equation –
 $ \Rightarrow 4x = 16 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ \Rightarrow x = \dfrac{{16}}{4} $
Find factors for the term on the numerator of the above expression.
 $ \Rightarrow x = \dfrac{{4 \times 4}}{4} $
Common multiple from the numerator and the denominator cancel each other.
 $ \Rightarrow x = 4 $ years
Hence, the age of John is $ 4 $ years.
So, the correct answer is “ $ 4 $ years.”.

Note: Be careful in converting the word statement in the mathematical expressions and also while simplification. Always remember, when you move any term from one side to another then the sign of the term changes. Positive terms become negative and the negative term becomes positive.