Question

5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that one pen by graphical method.
A. Cost of one pencil = Rs. 2 and that of one pen = Rs. 4
B. Cost of one pencil = Rs. 3 and that of one pen = Rs. 5
C. Cost of one pencil = Rs. 5 and that of one pen = Rs. 6
D. Cost of one pencil = Rs. 2 and that of one pen = Rs. 6

Answer 1

Hint: In this question use the given information to make the equations and remember to take the cost of pencil and pen as x and y respectively. Then by using the given information in the question, we will get two equations in terms of x and y. We just need to solve the equations by the graphical method to get the value of x and y.

Complete step-by-step answer:
According to the given information 5 pencils and 7 pens together cost Rs. 50
So let x be the cost of 1 pencil and y is the cost of 1 pen therefore the equation formed by the above equation is 5x + 7y = 50
$ \Rightarrow $5x = 50 – 7y
$ \Rightarrow $x = $\dfrac{{50 - 7y}}{5}$
$ \Rightarrow $x = $10 - \dfrac{{7y}}{5}$ (equation 1)
Putting the value of y = 5, 10, 15
Substituting the values of y in equation 1
For y = 5
x = $10 - \dfrac{{7 \times 5}}{5}$
$ \Rightarrow $x = 10 – 7
$ \Rightarrow $x = 3
Now for y = 10
x = $10 - \dfrac{{7 \times 10}}{5}$
$ \Rightarrow $x = 10 – 14
$ \Rightarrow $x = – 4
Now for y = 15
x = $10 - \dfrac{{7 \times 15}}{5}$
$ \Rightarrow $ x = 10 – 21
$ \Rightarrow $ x = – 11
So the required points are (3, 5), (-4, 10), (-11, 15)
Now by the given information the cost of 7 pencils and 5 pens together is Rs. 46
So the equation will be 7x + 5y = 46
$ \Rightarrow $5y = 46 – 7x
$ \Rightarrow $y = $\dfrac{{46-7x}}{5}$
$ \Rightarrow $y = $\dfrac{{46}}{5}-\dfrac{{7x}}{5}$ (equation 2)
Now using the value of x as 0, 2, 4
Substituting the values of x in the equation 2
For x = 0
y = $\dfrac{{46}}{5}-\dfrac{{7 \times 0}}{5}$
$ \Rightarrow $ y = $\dfrac{{46}}{5}$
$ \Rightarrow $y = 9.2
For x = 2
y = $\dfrac{{46}}{5}-\dfrac{{7 \times 2}}{5}$
$ \Rightarrow $ y = $\dfrac{{46}}{5}-\dfrac{{14}}{5}$
$ \Rightarrow $y = 6.4
For x = 4
y = $\dfrac{{46}}{5}-\dfrac{{7 \times 4}}{5}$
$ \Rightarrow $ y = $\dfrac{{46}}{5}-\dfrac{{28}}{5}$
$ \Rightarrow $ y = 3.6
So the require points are (0, 9.2), (2, 6.4), (4, 3.6)
Plotting the coordinates on the graph

So the value of x and y are (3, 5)
Thus the cost of pencil is Rs. 3 and the cost of pen is Rs. 5
Hence option B is the correct option.

Note:  In the above question was based on the concept of linear equation in 2 variable which can be explained as the equation which contains only 2 variable the general representation of linear equation in 2 variable is given as ax + by = 0 here a and b are the integers and x and y are the variable in the equation which means that its value is unknown, these equations have only 2 solution there are more types of equations such as linear equation of 1 variables which have only 2 dissimilarities than linear equation in 2 variable that are linear equations with 1 variables consist of 1 variables and it consists of only 1 solution.