A pair of boots was originally priced at $200. The store put them on sale for 25% off. A month later, the boots were reduced an additional 50% off the previous sale price. What is the price now?

$75

Step-by-step explanation:

$28.83

Step-by-step explanation:

We will use:   and then use cross multiplication.

Let's solve the first sale

We have:

percent = 25%

whole = $200

we want to solve for "part". Lets set the equation up before we plug anything in

now plug everything in:

part = $50

what does this mean?

Well it actually means $50 is the amount of money we take away from our original price of $200.

So we subtract that from our total.

$200 - $50 = $150

Next we will do the second sale.

percent = 50%

whole = $150

Use the same equation as above:

part = $75

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}