whats wrong in my calculation ?

[defeated_soldier]

once i had been to a post office to buy stamps of five-rupee, two-rupee and one-rupee. I paid the clerk Rs 20, and since he did not have change,he gave me three more stamps of one-rupee,If the number of stamps of each type that i had ordered initially was more than one,then what was the total number of stamps that i bought ?

Ans : 10

my solution....

let say, five-rupee note = x ,two-rupee note=y , one-rupee note =z

he got the retunn of 3 rs .(....but the clerk did not had change so he gave 3 one-ruppee stamp.)


so, 20-(5*x+2*y+z)=3

This gives x=2 ,y=3, z=1


so he got (2+3+1) + extra 3 stamps (in exchange of 3 rs)

Total=9


but answer given in the book is =10

WHATS WRONG IN MY CALCULATION ?

 

[galactus]

Try \(\displaystyle \L\\5x+2y+1z=20\)

Let's say you initially ordered 2-5's, 2-2's, and 3-1's. Remember, initially you ordered more than 1 of each. You have only 1-1 rupee ordered.

So you have 5x+2y+z=17

5(2)+2(2)+1(3)=17

You get back three more 1's

5(2)+2(2)+1(6)=20

2+2+6=10

You ended up buying 2-5's, 2-2's, and 6-1's.

Did I interpret the problem correctly?. Is this what you were looking for?.

 

[defeated_soldier]

thank you