Question

5 books and 7 pens together costs Rs 79 whereas 7 books and 5 pens together cost Rs 77. Find the total cost of 1 book and 2 pens.

Answer 1

Hint- Here, we will proceed by assuming the cost of 1 book and 1 pen as two different variables (say x and y respectively) and then we will form two linear equations in two variables and solve it by using elimination method.

Complete Step-by-Step solution:
Let us suppose that the cost of 1 book and 1 pen be Rs x and Rs y respectively
Given, Cost of 5 books and 7 pens = Rs 79
$ \Rightarrow $Cost of 5 books + Cost of 7 pens = Rs 79 $ \to (1)$
As we know that the cost of n items is given by
Cost of n items = n(Cost of 1 item) $ \to (2)$
Using the formula given by equation (2) in equation (1), we get
$ \Rightarrow $5(Cost of 1 book) + 7(Cost of 1 pen) = 79
$ \Rightarrow $5(x) + 7(y) = 79
Multiplying the above equation by 7 on both sides, we get
$
   \Rightarrow 7 \times 5x + 7 \times 7y = 7 \times 79 \\
   \Rightarrow 35x + 49y = 553{\text{ }} \to {\text{(3)}} \\
 $
Also, given that Cost of 7 books and 5 pens = Rs 77 $ \to (4)$
Using the formula given by equation (2) in equation (4), we get
$ \Rightarrow $7(Cost of 1 book) + 5(Cost of 1 pen) = 77
$ \Rightarrow $7(x) + 5(y) = 77
Multiplying the above equation by 5 on both sides, we get
.\[
   \Rightarrow 5 \times 7x + 5 \times 5y = 5 \times 77 \\
   \Rightarrow 35x + 25y = 385{\text{ }} \to {\text{(5)}} \\
 \].
By subtracting equation (5) from equation (3), we get
\[
   \Rightarrow 35x + 49y - \left( {35x + 25y} \right) = 553 - 385 \\
   \Rightarrow 35x + 49y - 35x - 25y = 168 \\
   \Rightarrow 24y = 168 \\
   \Rightarrow y = \dfrac{{168}}{{24}} = 7 \\
 \]
Put y = 7 in equation (3), we get
\[
   \Rightarrow 35x + 49\left( 7 \right) = 553{\text{ }} \\
   \Rightarrow 35x + 343 = 553{\text{ }} \\
   \Rightarrow 35x = 553 - 343 = 210 \\
   \Rightarrow x = \dfrac{{210}}{{35}} = 6 \\
 \]
So, the cost of 1 book and 1 pen are Rs 6 and Rs 7 respectively
 Cost of 1 book and 2 pens = Cost of 1 book + 2(Cost of 1 pen)
\[ \Rightarrow \]Cost of 1 bag and 10 pens = 6 + 2(7) = 6 + 14 = 20
Therefore, the cost of 1 book and 2 pens is Rs 20.

Note- In this particular problem, we have used elimination method for solving the two linear equations in which the coefficient of variable x is made same in both these equations by multiplying the first equation and second equation by 7 and 5 respectively so that when these equations are subtracted we will be just left with variable y in the final equation.