Question

a bag has total of 120 notes in denominations of 2 rs,5 rs and 10 rs. the total value of the notes in the bag is 760. if there were twice as many 5rs notes, then the total value of the notes would be 960. find the number of 10 rs notes in the bag?

Answer 1

OK start by coming up with some variables for how many of each type of note. Let's say

T=# of 2 notes
F=# of 5 notes, and
N=# of 10 notes

Now you can start writing some equations down. You know the total number of notes is 120, so how can you write that as an equation involving these 3 variables?

Answer 2

You also know that the total VALUE of the notes is 760. How can you express that as an equation? E.g., if I have T notes worth 2 rs each, then the total value of those notes is 2T, right? Now apply that to all 3 denominations and write the equation.

Answer 3

Finally, you also know that if there were twice as many 5rs notes, then the total value of the notes would be 960. So this will give you a 3rd equation, similar to the 2nd one, but should account for the fact that there aer TWICE AS MANY of the five notes (F), and the total value is 960.

So with those 3 equations, you have 3 equations in 3 unknowns and can start solving by substitution, work back and get values for all 3 of the variables.

Answer 4

if i apply it as you told then the first equation becomes 2t+5f+10n=120 right?

Answer 5

Wait, no....

Answer 6

Sorry - you are mixing up the equations. The 120 is the total NUMBER OF NOTES. The variables represent the NUMBER OF EACH TYPE of note. This first equation has NOTHING to do with the VALUE of each note.

Answer 7

The 2t+5f+10n will come into play when you get to the 2nd equation, the one that totals up the VALUE of the notes.

Answer 8

what if i assume total no. of notes of 2rs.5rs and 10 rs as x (one variable) and form the equation like 2x+5x+10x=120. so i will get the total no. of notes of each.?..but by doing so it becomes 120/17...and the no. of notes cannot be in decimals..

Answer 9

That equation assumes that you have the SAME number of each type of note. Nothing in the problem says that (and clearly it can't be true because the equation does not give an integer result).

The way I explained is the way to do it. It would be convenient and faster if you could do it in 1 equation, but you can't. You need 3. :)

Answer 10

can u tell me those three equations?..i m a little confused.

Answer 11

Well, you almost have the first one. But like I said - you are looking for the total of the NUMBER of the notes. The variables represent the number of each TYPE of note. So this equation does not involve the VALUES, just the NUMBER of each.

You have T 2's, F 5's, and N 10's, and altogether you have 120. So the sum of T, F, and N is 120. How do you write that as an equation?

Answer 12

2T+5F+10N=120 right? but how do i form equation for the values of notes in bag i.e for 760? or 960?

Answer 13

Nooo... you are still involving the VALUES of the notes in the wrong equation. The QUANTITY of each note type is given by the variables. The TOTAL quantity is 120. SO:

T+F+N=120

Do you see why, and how that is different from your equation?

Answer 14

2T+5F+10N is:

2 times the # of 2 rs notes = total value of the 2's, PLUS
5 times the # of 5 rs notes = total value of the 5's, PLUS
10 times the # of 10 rs notes = total value of the 10's

So that sums to the total value of the all the notes!

Do you see the difference between this and the first equation? This is an IMPORTANT distinction.

Answer 15

ooh ya bt...now how do i form 2nd and third equation...as we have assumed T,F and N as no. of notes..then how can we form the equation involving total values of notes (i.e 760rs)??

Answer 16

what equations have you figured out so far ?

Answer 17

T+F+N=120 just one.

Answer 18

ok, that one looks good.

How much money do you have if you have T of the 2 rs notes ?

Answer 19

Like I said:

2T+5F+10N is:

2 times the # of 2 rs notes = total value of the 2's, PLUS
5 times the # of 5 rs notes = total value of the 5's, PLUS
10 times the # of 10 rs notes = total value of the 10's

So that sums to the total value of the all the notes!

Now, can you make that into the 2nd equation? The one for the total value of 760?

Answer 20

ok now i got it..so i ll have 2 equations like T+F+N=120 for total no. of notes and 2T+5F+10N=760 right?? and accordingly 3rd will be 2T+(2*5F)+10N=960..is it correct?

Answer 21

perfect

Answer 22

I would use elimination to solve
this system of equations

Answer 23

Here is an example of how to do it
http://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/matrices_elimination/v/matrices--reduced-row-echelon-form-1

Answer 24

Thanks debbieG it was very helpful.

Answer 25

and ya i will go through dat example u have given phi..thnks..

Answer 26

You're welcome, and like @phi said, if you've done matrices you could go that route. Otherwise, you can manage it by just back-substituting but it's a bit more tedious. :)