Acash register contains $5 bills and $50 bills with a total value of $1060. if there are 32 bills total, then how many of each does the register contain?

12 5 dollar bills

20 50 dollar bills

Step-by-step explanation:

Let x = number of five dollar bills

Let y = number of fifty dollar bills

We have a total of 32 bills

x+y = 32

The total amount is 1060

5x+50y = 1060

We have 2 equations and 2 unknowns

x+y = 32

5x+50y = 1060

Multiply the first equation by -5 so we can eliminate x

-5x -5y = -5*32

-5x -5y =-160

Add this to the second equation

5x+50y = 1060

-5x -5y =-160

45 y    = 900

Divide each side by 45

45y/45 = 900/45

y = 20

There are 20 50 dollar bills

x+y = 32

x+20 = 32

Subtract 20 from each side

x+20-20 = 32-20

x = 12

There are 12 5 dollar bills

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

add an image

step-by-step explanation: