# algebra

posted by .

Money Mixtures. Elaine has \$194, consisting of \$20, \$5, and \$1 bills. The number of \$1 bills is 1 less than the total number of \$20 and \$5 bills. If she has 39 bills in her purse, how many of each denomination does she have?

• algebra -

I have already solved two problems like this for you. Set up the algebraic equations that describe what you know, and solve them. There will always be as many independent equations as there are unknowns.

• algebra -

number of \$20's ---- x
number of \$5's ----- y
number of \$1's ----- z

but z = x+y - 1

x+y+z = 39
x + y + x+y-1 = 39
2x + 2y = 40
x + y = 20 (#1)

also

20x + 5y + z = 194
20x + 5y + x+y-1 = 194
21x + 6y = 195
7x + 2y = 65 (#2)

double #1 and subtract fron #2
5x = 25
x = 5
then in x+y = 20 , ----> y = 15
and finally
z = x+y-1 = 19

check: is 5+15+19 = 39 ? YES
is 20(5) + 5(15) + 19 = 195 ? YEA!!

## Similar Questions

1. ### math

Joseph sold tickets to the school musical. He had 12 bills worth \$175 for the ticketssold. If all the money was \$5 bills, \$10 bills, and \$20 bills, how many of each bill did he have?
2. ### Pre Calculus

A bank teller is counting the total amount of money in a cash register at the end of the day. There is a total of \$2600 in denominations of \$1, \$5, \$10 and \$20 dollar bills. The total number of paper bills is \$235. The number of twenty …

A bank teller is counting the total amount of money in a cash register at the end of the day. There is a total of \$2600 in denominations of \$1, \$5, \$10 and \$20 dollar bills. The total number of paper bills is \$235. The number of twenty …
4. ### algebra

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 7more than the number of \$5. How many bills of each denomination?
5. ### Math

Mr. Singh deposited \$170 in his bank. The number of \$5 bills was three times the number of \$10 bills and the number of one dollar bills was 30 more than the number of five dollar bills how many bills of each type did he deposit
6. ### Algebra

For a board game there is 3 kinds of bills. There are 11 more \$2 bills than \$1 dollar bills. There are 18 fewer \$3 dollar bills than \$1 bills. The total for the bill is \$100. How many \$1 bills are used?
7. ### Highland

A cash register has no one dollar bills and all of the bills are five dollar bills \$10 bills or \$20 bills they are a total of 37 in the cash register and the total value of his bills is &310 if the number of the \$10 bill in the register …
8. ### Algebra: Avc

A cash register has no one dollar bill in it all of the bills are five dollar bills \$10 bills or \$20 bills there are a total 37 bills in the cash register and the total value of this bills is \$310 if the number of \$10 bills in the …
9. ### Algebra

A wallet contains \$445 in \$5, \$10, and \$20 bills. The number of \$5 bills exceeds the number of \$10 bills by 2, and the number of \$20 bills is 3 less than twice the number of \$10 bills. How many bills of each type are there?
10. ### Algebra

wallet contains \$290 in \$5, \$10, and \$20 bills. The number of \$5 bills exceeds the number of \$10 bills by 4, and the number of \$20 bills is 3 less than twice the number of \$10 bills. How many bills of each type are there?

More Similar Questions