Question

A bank teller has 35 bills in $5,$10, and $20 denominations. The total value from these bills is $370. The total number of $10 bills and $20 bills is 7 more than the number of $5. How many bills of each denomination does the teller have?

Answer 1

The first thing that I'm doing here, which I'm not sure if its on the right track, but:
I looked for two numbers with a difference of 7 that when added up will give you 35, since that is the total number of bills and the problem states that "the total number of 10 bills and 20 bills is 7 more than 5 bills"

so the numbers I'm using after trying different ones are

14 and 21
where there are 14 $5bills and 21 of both $10 and $20 bills

Answer 2

I'ma make a small drawing and send it

Answer 3

okay

Answer 4

ok, this is the first drawing, the little half circles represent $10 dollar bills and there are 21. ...

Answer 5

At first I pretended as if there were only $10 bills, giving me a total of 210 out of the 300. Leaving me short by 90
so what I did then is I added the other half circle so that instead of the half circle= 10, the now circle=20.

Now though the value is of 220, we are now off by 80

and I continued to do that until I got 300 as my final answer.

Do you understand me?... I sometimes can't explain myself well, but I can try

Answer 6

I understand you a little

Answer 7

So not exactly right :p

Answer 8

yeah

Answer 9

jaja its cool :p

well do you see what I did in the very beginning? how I figure out that there were 14 5 dollar bills?

Answer 10

lol, yeah I get that part

Answer 11

ok, well from what I meant with my drawings was this:

as you can see on the first drawing:
all 21 bills(half circles are worth $10)
so I had said that if all 21 bills are 10s then the total value of the 35 bills that we have is
70 (from the 5's) + 210 (from the 21 10's)
= 280 and leaves us short by $90 so
14 $5's 21 $10's and 0 $20's is not the bills she has.

technically she has to have atleast 1 20 since she mentions she has it.
so actually between the 21 bills of 10s and 20s, 1 of them is a 20

70 + 200 (20 10s) + 20( one twenty)= 290

and that leaves us short by $80...

now though, since its not 370 as we like it to be there must be more 20s and less 10s so what I did

I made a bill out of the 20 bills left of value $10 into 20
so now there are 19 ten dollar bills and 2 twenty dollar bills
190+40=230 plus the 70 of the 5 =300 leaving us $70 short
so I did the process again. and continued to do it until I get the whole 370 i need

Understand me now?

Answer 12

Yes okay gotcha

Answer 13

okay :D... Once you have the bills for each value you can ask me if you'd like; to see if our answers match.

Answer 14

okay i get back to you

Answer 15

did you get -365/2, 1227/4, -357/4 if like i did something wrong

Answer 16

um..no I didn't get that.. what you do? how did you get negatives?
btw, I found a shorter way to do it, based on algebra... but lets see what you did first. Could you show me your step pls

Answer 17

5x+10y+20z=370, x+y+z=35, 10y+20z=7+5x some where i went wrong i guess

Answer 18

um... I do think that the 10y+20z=7+5x was the problem

What I was doing above was not algebra, probably elementary math lol.. and I think that if we do it that way it would look something like this:
y+z+7=x

Answer 19

where like you said x+y+z = 35

Answer 20

but then we have many variables to solve... **** and sorry it be more like y+z-7=x

Answer 21

lol it's okay

Answer 22

this is what I would have done algebraically:
I would have still done the whole thing I did first in trying to get how many 5s there were so there were 14 5s and a total of 21 10s and 20s

so then y+z=21
and y=21-z
and since 370-70=300
10y+20z=300
now, I'd plug in for the new y

10(21-z)+20z=300
then just solve for z and you'll get how many 20s there are

Answer 23

okay

Answer 24

oh! and you gave me an idea of how to solve for the 5s instead of guessing

let x be the dollar bills for 5's

so then
x+(x+7)=35
where x+7 represents the number of bills for 10s and 20s
see how?

one you solve for x, you still get 14

Answer 25

So if you use the thing from the message right above this one, followed by the message where I solved for z, then you'll get the answer. Sorry for so many turns here and there; but finally we have arrived to the destination. Any questions?

Answer 26

i get 16, 9, 10 what about you

Answer 27

and thanks for your time

Answer 28

uh, I got 14, 12, 9... :o..

Answer 29

it can't be what you got since 9+10=19 and 19 is not 7 more than 16

Answer 30

are you sloving by 3 by 3 system of equations i lead you in the wrong direction

Answer 31

I don't understand what you are asking me. but basically what I solved for was for how x y and z (5s 10s and 20s)

Answer 32

what i did for the last equation was set it up as x-y=7

Answer 33

I see what your doing thanks lol. Sorry about that

Answer 34

You kinda lost me.. lol... do you know what to do now??? and you'd be doing wrong by doing x-y=7...

Answer 35

yes I shouldn't have switch and changed the signs. I see how you did it.

Answer 36

I see.. well hope you got, it... I still feel confused with what you said, but I think you understood the problem with what you are writing lol...