if 5 pencil cost 15 rupees and 2 eraser cost 5 rupees what is the cost of one pencil and eraser options here
(a rs7.50) (b rs 5.50) (c rs 15) (d rs 10)
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The total cost of 2 pencils, 5 erasers and 7 sharpeners is Rs 30, while 3 pencils and 5 sharpeners cost Rs 1.5 more than 6 erasers. By what amount (in Rs) does the cost of 39 erasers and 1 sharpener exceed the cost of 6 pencils?
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3 Answers
Profile photo for Panna Lal Patodia
Panna Lal Patodia, I am a software engineer from BITS, Pilani and mathematics is my hobby.
Answered July 19, 2018
Assume the cost of a Pencil is x, cost of Eraser is y and cost of Sharpener is z.
Then, cost of 2 pencils, 5 erasers and 7 sharpeners is Rs. 30. Thus,
2x + 5y + 7z = 30 …. (1)
Further, given cost of 3 pencils and 5 sharpeners is Rs. 15 (Assuming Rs. 1.50 is typo) more than 6 erasers. So,
3x + 5z = 6y + 15
3x - 6y + 5z = 15 …. (2)
Now, we need to find the difference of cost between 39 erasers + 1 sharpener and cost of 6 pencils. Thus, we need to compute 39y + z - 6x.
If we multiply Equation (1) by 3 and Equation (2) by -4 and then add these, we get:
-6x + 39y + z = 30.
So, the answer is Rs. 30.
Important Note: Generally, to solve equations in 3 unknowns, we require 3 equations. However, here the third equation can be derived from first 2 equations, so two equations are sufficient to find the answer. But, these equations are insufficient to find the cost of pencil, eraser or sharpener.