A cashier has a total of 34 bills, made up of ones, fives, and twenties. The number of fives is one less than the number of twenties. The total value of the money is $237. How many of each denomination of bills are there? (Hint: Let x = the number of ones, y = the number of fives, and z = the number of twenties).

Question

Reiny · Answer

Not going to follow the hint, why use 3 unknowns?
I think the following way is easier:

number of twenties -- x
number of fives ------ x-1
number of ones = 34 - x - (x-1)
= 35 - 2x

20x + 5(x-1) + 35-2x = 237
23x = 207
x = 9

So we have 9 twenties, 8 fives, and 17 ones

check:
they do add up to 34
value: 9(20) + 8(5) + 17 = 237
All is good!

Bob · Answer

^ where do you get the 35 and 2x?

Bob · Answer

34 - x - (x-1) 34 - x + x + 1 34 - 2x + 1 35 - 2x correct?

Lindsey · Answer

we have to have three equations. as this is a system of equations and inequalities problem. I have this so far:

x=# of 1's
y=# of 5's
z=# 20's

and I have the following equations.

1x+5y+20z=237
x+y+z=34

and I need another equation. but I am having trouble doing it. the teacher stated to use the hint as an equation but I am having trouble putting it together