Question

sanjay bought 5 notebooks and 2 pens for rs.120 he told that to guess the cost of each notebook and pen to his friends mohan and anil .sanjay has given the clue that both the costs are integers and divisible by 5 such that the cost of a notebook is greater than that of pen .now mohan and anil tried to guess .mohan sais that price of each notebook could be rs.18 then 5 notebook would cost be Rs.90 the two pens wouldbcost be 30 and each pen could be rs.15 anil felt that rs.18 for one noyebook was too little it should be least rs.20 then the price of each pen would also be rupees 10.based on the above situation answer the following questions (i) write a linear equations in two variables for the situation (ii)draw the graph for this so (iii) check whether the answers of mohan and anil are correct (iv) find the cost of a notebook and a pen​

Answer 1

Given : Sanjay bought 5 notebooks and 2 pens for Rs. 120.  

both the costs are integers and divisible by 5

cost of a notebook is greater than that of a pen.

Mohan said that price of each notebook could be Rs. 18. Then five notebooks would cost Rs.90, the two pens would cost Rs.30 and each pen could be for Rs. 15

Anil felt that Rs. 18 for one notebook was too little. It should be at least Rs. 20. Then the price of each pen would also be Rs.10

To Find :  (i) Write a linear equation in two variables for this situation

(ii) Draw the graph for this situation.

.(iii) Check whether the answers of Mohan and Anil are correct

.(iv) Find the cost of a notebook and a pen.​

Solution:

both the costs are integers and divisible by 5

Cost of Note book  = 5X

Cost of Pen = 5Y

and X > Y  >  0

Sanjay bought 5 notebooks and 2 pens for Rs. 120.  

=> 5 *5X  + 2(5Y)  = 120

=> 5X + 2Y  = 24

5X + 2Y  = 24

=> 5X = 24 - 2Y

=> 5X  = 2(12 - Y)

X must be multiple of 2  and 12 - Y must be multiple of 5

=> Y can be 2 or  7  

Y = 2  => X = 4

Y = 7  => X = 2   not possible as X > Y

=> Y = 2  => X = 4  is only possible solution

Cost of Note book  = 5*4 = 20

Cost of Pen = 5Y = 5 * 2 = 10

answers of  Anil are correct

Mohan is not correct as price 18 of note book is not divisible by 5

Cost of a Note book  = Rs 20

Cost of a Pen = Rs 10

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