a cashier has 25 bills consisting of twice as many ones as tens, two fewer fives than ones and the rest twenties. If the total value is $140 find how many of each she has using one variable

Answer 1

Let w = # of ones,

x = # of fives,

y = # of tens,

z = # of twenties

So, w + x + y + z = 25

(There are 25 bills in total)

Twice as many ones as

tens, so w = 2*y =2y

# of fives is 2 less than

number of ones, so

x = w - 2 or in terms of y...

x = 2y - 2

# of tens is y

The rest is twenties (z).

Need to solve for z in

terms of y.

w + x + y + z = 25

2y+(2y-2)+y+z =25

5y - 2 + z = 25

5y + z = 27

z= 27 - 5y

The value of all the bills is

$140, so...

1*w + 5*x + 10*y +20*z =140

1(2y)+5(2y-2)+10y+20*(27-5y)=140

2y+10y-20+10y+540-100y=140

-78y + 530= 140

-78y = -390

y = 5 (number of tens)

Everything is in terms of y,

so substitute back in for y

to find the other bills.

w=2y, x=2y-2, z=27-5y

Don't forget to check that

the value of all the bills adds

to $140.