[ikryspy]

I have two problems that I don't understand, so if anybody can help, that would be wonderful.

We are doing word problems with system equations with three variables
THE SET UP:
a.___variables__
b.__equation 1__
__equation 2__
__equation 3__
c.__x=,y=,z=___

THIS IS WHAT I HAVE SO FAR; OBVIOUSLY NOT MUCH.

1.)Mrs. Thompson has one-dollar, five-dollar, and ten-dollar bills that total $171. She has the same number of five-dollar bills as one-dollar bills and ten-dollar bills put together. If she has 30 bills in all how many bills of each denomination does she have?
a.) ___x=$1, y=$5, z=$10___
b.)__x+y+z=171___________
_______________________
_______________________
c.)_______________________


2.) John has 31 coins consisting of quarters,dimes, and nickles. If he had one more dime, he would have just as many dimes as he has nickles and quarters put together. If the total value of John's coins is $4.70, how many coins of each kind does he have?
a.___q=quarters,d=dimes,n=nickles__
b.__q+d+n=31____________________
_______________________________
__.25q+.1d+.05n=4.70____________
c.________________________________


PLEASE HELP!
BTW what I have there I'm not exactly sure its right --- thanks.

[eeseely]

Here's some help with your 2nd problem:

If he had one more Dime, he would have just as many Dimes as he has Nickels and
Quarters.

Using N, D and Q for number of Nickels, Dimes and Quarters, this statement translates to:

D = N+Q-1 (1)

Also, N+D+Q = 31 (2)

Substituting for D in (2) yields: N+(N+Q-1)+Q = 31

2(N+Q) = 32 and N+Q = 16

Then, from (1) above, D = 15

5N+10D+25Q = 470

5N+(10)(15)+25Q = 470

5N+150+25Q = 470

5N+25Q = 320

N+5Q = 64 (3)

From (1), N = 15-Q+1 = 16-Q

Substituting for N in (3) yields:

16-Q+ 5Q = 64

4Q = 48

Q = 12; D = 15; N = 4

[eeseely]

Here's some help on your Problem 1.:

Mrs. Thompson has one-dollar, five-dollar, and ten-dollar bills that total $171.

$1x+$5y+$10z = $171 (1)

She has the same number of five dollar bills as one dollar bills and ten dollar bills put together.
This is represented by:

y = x+z (2)

If she has 30 bills in all, how many bills of each denomination does she have?

x+y+z = 30 (3)

Let x, y, z be the number of $1-, $5- and $10-bills, respectfully.

Can you take it from there?

[ikryspy]

Thank you sooo! Much, I didn't think I was ever going to figure this out. Your help is really appreciated.