Question

Sekhar gives a quarter of his sweets to Renu and then gives five sweets to Raji. He has \[7\] sweets left. How many did he have to start with?

Answer 1

Hint: In the given question, we are required to write an algebraic equation based on the information given to us. First, break down the information given to us to try and identify what algebraic equations must look like. We will introduce some variables and form an algebraic equation and then try to solve the equation using the transposition method.

Complete step-by-step solution:
So, in the question, we are given that Sekhar gives a quarter of his sweets to Renu and five to Raji and is still left with seven sweets. Now, we are required to find the initial number of sweets with Sekhar.
 So, we will introduce a variable and let the number of sweets with Sekhar be x.
Then, he gives a quarter to Renu.
So, $\dfrac{x}{4}$ sweets are given to Renu.
Now, he gives five sweets to Raji and seven sweets are still left with him.
So, mathematical equation can be formed as: $x - \dfrac{x}{4} - 5 = 7$
Now, we will solve the above equation to find the value of x using the transposition method.
So, adding five to both sides of equation,
$ \Rightarrow x - \dfrac{x}{4} - 5 + 5 = 7 + 5$
Adding up the like terms, we get,
$ \Rightarrow \dfrac{{3x}}{4} = 12$
Multiplying both sides of the equation by $\dfrac{4}{3}$. So, we get,
$ \Rightarrow \dfrac{4}{3} \times \dfrac{{3x}}{4} = \dfrac{4}{3} \times 12$
Cancelling the common factors in numerator and denominator, we get,
$ \Rightarrow x = 16$
So, the value of x in the equation is $16$. Hence, Sekhar has $16$ sweets in the starting.

Note: When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of a mathematical symbol is called a mathematical expression. If there is an equal $\left( = \right)$ sign in the expression, then it is called an equation. Method of transposition can be used to solve any mathematical equation.