Question

The cost of five pens, eight erasers and eleven sharpeners is ₹54. The cost of 3 pens, 5 erasers and 7 sharpeners is ₹34. Find the cost of one pen, one eraser and one sharpener.

Answer 1

Hint: In the given question, there are 3 unknown values. Let the cost of one pen be x, cost of one eraser be y and cost of one sharpener be z and then proceed as the question says.

Complete step-by-step answer:
Let the cost of one pen be $x$ , one eraser be $y$ and one sharpener be\[z\].
It is given that the cost of 5 pens, 8 erasers and 11 sharpeners = ₹54
$ \Rightarrow 5x + 8y + 11z = 54$ ………………………………………………………………………………………………………….. Eqn 1
It is also given that the cost of 3 pens, 5 erasers and 7 sharpeners = ₹34
$ \Rightarrow 3x + 5y + 7z = 34$ …………………………………………………………………………………………………………… eqn 2
Now,
On Multiplying eqn 1 with 2 and eqn 2 with 3 we get,
 $ \Rightarrow 10x + 16y + 22z = 108$ …………………………………………………………………………………………………… eqn 3
$ \Rightarrow 9x + 15y + 21z = 102$ …………………………………………………………………………………………………….. Eqn 4
On subtracting eqn 4 from eqn 3 we get,
$
   + (10x + 16y + 22z = 108) \\
  \dfrac{{ - (9x + 15y + 21z = 102)}}{{x + y + z = 6}} \\
 $
Hence,
 The cost of one pen, one eraser and one sharpener i.e. $x + y + z$ is equal to ₹6.

Note: For a system of 2 unknown variables, if we have to find the values of 2 unknowns we have to form 2 linear equations in 2 variables. Similarly, for a system of 3 unknown variables, we have to form 3 linear equations in 3 variables to find the values of unknowns and so on.