Question

Irfan says that he has $ 7 $ marbles more than five times the marbles Parmit has, Irfan has $ 37 $ marbles. How many marbles does Parmit have?

Answer 1

Hint: Here we will first assume the unknown number of marbles of Parmit be “x” and then will convert the given word statements in the form of the mathematical expressions and will simplify for the resultant value for “x”.

Complete step by step solution:
Let us assume the number of marbles with Parmit be “x” marbles
Given that: Irfan says that he has $ 7 $ marbles more than five times the marbles Parmit has, Irfan has $ 37 $ marbles.
Convert the above word statements in the form of the mathematical expressions.
 $ 7 + 5x = 37 $
Move the constant term on the opposite side, when you move any term from one side to the other then the sign of the terms also changes. Positive term changes to the negative term.
 $ 5x = 37 - 7 $
Simplify the above expression finding the difference of the terms on the right hand side of the equation.
 $ 5x = 30 $
Term multiplicative on one side if moved to the opposite side then it goes to the denominator.
 $ x = \dfrac{{30}}{5} $
Find factors of the term on the numerator.
 $ x = \dfrac{{6 \times 5}}{5} $
Common factors from the numerator and the denominator cancel each other.
 $ x = 6 $
Hence, Parmit has $ 6 $ marbles.
So, the correct answer is “6”.

Note: Be careful about the sign convention while simplification especially while moving any term from one side to another. When you move any term from one side to another then the sign of the term changes. Positive term changes to the negative term and vice-versa. Always remove common factors in the expression of the fraction for the simplified form.