Question

3 pens, 5 pencils and 7 erasers cost Rs. 49 while 5 pens ,8 pencils and 11 eraser cost Rs. 78 . find the cost (in Rs.) of 3 pen, 3 pencils and 3 erasers ?

Answer 1

Let cost of each pen, pencil and eraser be Rs. x, y and z respectively, then
3x + 5y + 7z = 49 ---(i) and
5x + 8y +11z =78 ---(ii)
Multiplying eqn. (i) by 5 & (ii) by 3 and then subtracting (ii) from (i), we get y + 2z = 11 ---(iii)
Here (y,z) satisfying condition can be (1,5) (3,4) (5,3) (7,2) (9,1)
But only y=5, z=3 with x=1 satisfies the condition in eqn (i) or (ii)
So cost of 3 pen, 3 pencils and 3 erasers = 3x+3y+3z = 3(x+y+z) = 3(1+5+3) = Rs. 27
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Answer 2

Answer:

Let cost of each pen, pencil and eraser be Rs. x, y and z respectively, then

3x + 5y + 7z = 49 ---(i) and

5x + 8y +11z =78 ---(ii)

Multiplying eqn. (i) by 5 & (ii) by 3 and then subtracting (ii) from (i), we get y + 2z = 11 ---(iii)

Here (y,z) satisfying condition can be (1,5) (3,4) (5,3) (7,2) (9,1)

But only y=5, z=3 with x=1 satisfies the condition in eqn (i) or (ii)

So cost of 3 pen, 3 pencils and 3 erasers = 3x+3y+3z = 3(x+y+z) = 3(1+5+3) = Rs. 27