Each Saturday, a store reduces the price of any unsold item by

10%. If an item was priced at $80, on Saturday of the first week it

is marked down to $72. At the end of the second week, it drops

to $64.80, and at the end of the third week the price is decreased

to $58.32. If this continues for 10 weeks, what should be the

selling price for an item that was originally priced at $80?

a-$27.89

b-$30.99

c-$52.11

d-$8.00

The correct option is a-$27.89

The selling price for an item would be $27.89 after the 10th week which was originally priced at $80.

Step-by-step explanation:

Each week, a store reduces the price of any unsold item by 10%

If this continues for 10 weeks, what should be the selling price for an item that was originally priced at $80?

The reduced price of the unsold item is given by

Initial price × (1 – discount) ⁿ

Where discount is 0.10 and n is the week number

After 1st week:

$80(1 - 0.10)¹

$80(0.90)¹

$72

After 2nd week:

$80(1 - 0.10)²

$80(0.90)²

$64.80

After 3rd week:

$80(1 - 0.10)³

$80(0.90)³

$58.32

Similarly, we can find the price of the unsold item for the 10th week by substituting n = 10

After 10th week:

$80(1 - 0.10)¹⁰

$80(0.90)¹⁰

$27.89

Therefore, the selling price for an item would be $27.89 after the 10th week which was originally priced at $80.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1