Question

If 15 oranges cost Rs.40, what is the cost of \[3\] dozen oranges?

Answer 1

Hint: To solve this question we just need the knowledge of how to convert a problem statement into mathematical form. This question can be simply solved by simple multiplication and division. The application of linear equations in one variable in this question can make our task easy and we can easily get our required answer. In this question find the cost of one orange and accordingly get it for \[3\] dozen oranges.

Complete step-by-step solution:
This question requires the knowledge of linear equations in one variable and how to apply it on the given problem statement. We should also know what a dozen indicates in a mathematical number. The knowledge of simple mathematical operations can help us to easily solve the given question. Let us now discuss the required concepts one by one.
Linear equations in one variable: The equations consisting of only one variable with index (highest power) \[1\] are known as linear equations in one variable. There is only one variable present in these types of equations. To solve linear equations in one variable we should know basic mathematical rules and operations. We can write the given problem statement in terms of mathematical expressions which are more familiar to us by using linear equations in one variable.
For e.g. \[x-1=0\] is a linear equation in one variable.
Here,\[x\] is the variable
By solving we get,
\[x=1\] is the solution of the above linear equation in one variable .
To solve this question we should know that \[1\] dozen oranges are equal to \[12\] oranges.
After revising all the required concepts we will now solve the main question.
We have been given that the cost of \[15\] oranges is Rs. \[40\].
We have to find the cost of \[3\] dozen oranges.
Let, \[x\] be the cost of one orange.
Hence, the required linear equation in one variable is given by,
 \[15x=40\]
\[\begin{align}
  & \Rightarrow x=\dfrac{40}{15} \\
 & \Rightarrow x=\dfrac{8}{3} \\
 & \Rightarrow x=2.66 \\
\end{align}\]
Hence, the cost of one orange is Rs.\[2.66\].
Now, \[3\] dozen oranges\[=12\times 3=36\] oranges
Let, \[C\] be the cost of \[3\]dozen oranges.
\[\begin{align}
  & \Rightarrow C=36x \\
 & \Rightarrow C=36\times 2.66 \\
 & \Rightarrow C=36\times \frac{8}{3} \\
 & \Rightarrow C=12\times 8 \\
 & \Rightarrow C=96 \\
\end{align}\]
From this we can conclude that the cost of \[3\] dozen oranges is Rs.\[96\].

Note: These types of questions just need the knowledge of conversion of word problem or problem statement into mathematical form. By solving linear equations in one variable we can get the perfect answer if we apply all the concepts properly. This question does not require lengthy calculations and can be solved in a few number of steps.