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Arnav’s father is 49 years old. He is nine years older than four times the Arnav’s age. Set up an equation to find Arnav’s age.

Last updated date: 13th Jun 2024
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Hint: We should first read the question & try to relate Arnav’s age with that of his father. Here, age of Arnav’s father is to be derived from that of Arnav according to the question so Arnav’s age should be assumed first. Then we will have to form a linear equation of their relation to solve this problem.

Complete step-by-step answer:
Let us assume the age of Arnav be $x$ years.
Then, four times of Arnav’s age will be $4x$ years.
Then, nine years older than that will be - $4x + 9$ years
Since, as per question, Arnav’s father age is\[\;49\] years, then,
 $49 = 4x + 9$ - Equation to find age of Arnav .
Or, $4x + 9 = 49$ [ taking all numerical terms in one side of = sign ]
 or, $x = \dfrac{{49 - 9}}{4} = 10years$
The above is the equation for finding Arnav’s age and Age of Arnav is \[10{\text{ }}years.\]

Additional Information:
Whenever these kinds of problems are found, understand the question & form a linear equation. By definition, an equation is a mathematical statement arranged such that two different mathematical expressions are equal to each other.

Note: In this type of problem, we have to consider/assume ‘x’ to the term which is to be asked. Here, Arnav’s age should be obtained, so it is assumed to x and then proceed. As per condition given in the question, form an equation & solve it to get the age of Arnav. Do the calculations carefully to avoid the silly mistake. Do not forget to write units (here years) because a no. without unit is meaningless.