Question

The cost of a chocolate is Rs. \[\left( {x + 4} \right)\] and Rohit bought \[\left( {x + 4} \right)\] chocolates. Find the total amount paid by him in terms of \[x\]. If \[x = 10\], find the amount paid by him.

Answer 1

Hint: Here, we need to find the total amount paid by him in terms of \[x\]. The total amount paid by him is the product of the number of chocolates bought and the cost of each chocolate. We will therefore multiply the cost of the chocolate with the total to get a quadratic equation. We can simplify the equation to get the amount paid by him in terms of \[x\]. We can then substitute the value of \[x\] to find the amount paid.

Complete step-by-step answer:
First, we will find the total amount paid by Rohit in terms of \[x\].
The total amount paid by Rohit is the product of the number of chocolates bought and the cost of each chocolate.
We know that Rohit bought \[\left( {x + 4} \right)\] chocolates and the cost of each chocolate is Rs. \[\left( {x + 4} \right)\].
Therefore, we get
\[{\rm{Amount\, paid\, in\, terms\, of }}x = \left( {x + 4} \right)\left( {x + 4} \right)\]
Now, we will simplify the expression on the right side of the equation.
Multiplying the terms using the distributive property, we get
\[ \Rightarrow \left( {x + 4} \right)\left( {x + 4} \right) = {x^2} + 4x + 4x + 16\]
Adding the like terms, we get
\[ \Rightarrow \left( {x + 4} \right)\left( {x + 4} \right) = {x^2} + 8x + 16\]
Therefore, the amount paid by Rohit in terms of \[x\] is Rs. \[{x^2} + 8x + 16\].
Now, we will find the total amount paid by Rohit if the value of \[x\] is 10.
Substituting \[x = 10\] in the expression, we get
\[{\rm{Amount\, paid\, by\, Rohit}} = {10^2} + 8\left( {10} \right) + 16\]
Simplifying the expression, we get
\[{\rm{Amount\, paid\, by\, Rohit}} = 100 + 80 + 16 = 196\]
\[\therefore\] The amount paid by Rohit is Rs. 196 if \[x = 10\].

Note: We should remember the method to obtain the total cost. It is important to keep in mind that the total cost can be found by multiplying the number of chocolates with the cost of one chocolate. If instead of multiplying we divide the terms then we will get the wrong answer. We usually divide the total cost with the total number of units to find the cost of one unit. As we have to find the total cost we will multiply and divide the terms. Here we have used distributive property but we can also use the algebraic identity for the square of two numbers \[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\] to find the product \[\left( {x + 4} \right)\left( {x + 4} \right)\] .