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The total cost of 8 books and 5 pens is 420 rupees and the total cost of 5 books and 8 pens is 321 rupees. Find the cost of 1 book and 2 pens.

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Last updated date: 29th Mar 2024
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MVSAT 2024
Answer
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Hint: In this question we need to find the cost of 1 book and 2 pens. Assume that the cost of 1 pen and 1 book to be a variable. Formulate linear equations in two variables using the information provided in the question by computing cost on both sides of the equation. Solve these equations to get the desired variables.

Complete step-by-step answer:
Let the cost of 1 book be x Rupees.
And the cost of 1 pen is y Rupees.
Now it is given that the cost of 8 books and 5 pens is 420 Rupees.
So construct the linear equation according to given information we have,
$ \Rightarrow 8x + 5y = 420$…………………………. (1)
Now it is also given that the cost of 5 books and 8 pens is 321 Rupees.
So again construct the linear equation according to given information we have,
$ \Rightarrow 5x + 8y = 321$…………………………. (2)
Now solve these two equations using a substitution method.
So calculate the value of x from equation (1) and substitute in equation (2) we have,
$ \Rightarrow x = \dfrac{{420 - 5y}}{8}$………………… (3) Substitute this value in equation (2)
$ \Rightarrow 5\left( {\dfrac{{420 - 5y}}{8}} \right) + 8y = 321$
Now simplify the above equation we have,
$ \Rightarrow 2100 - 25y + 64y = 2568$
$ \Rightarrow 39y = 468$
Now divide by 39 throughout we have,
$ \Rightarrow y = \dfrac{{468}}{{39}} = 12$ Rupees.
Now from equation (3) we have,
$ \Rightarrow x = \dfrac{{420 - 5\left( {12} \right)}}{8} = \dfrac{{420 - 60}}{8} = \dfrac{{360}}{8} = 45$ Rupees.
So the cost of 1 book is 45 Rupees and the cost of 1 pen is 12 Rupees, hence we need to find the cost of two pens so it will be $12 \times 2 = 24$.

Note: Whenever we face such types of problems the key concept is to use various methods to solve the linear equation in two variables which is formed using the question’s information. The methods that can be used are elimination or substitution. In the above solution substitution is being used. This concept will help you to find out the solution.