A furniture store is having a sale on couches that cost $1000 or more. A 10% discount will be applied. If a couch that has an original cost of $2000 is purchased, what will the final cost be after the 10% discount is applied? *

200%

Step-by-step explanation:

because 2000 is more than 1000 so the discount is 10% and 10% of 2000 is 200

$1800

Step-by-step explanation:

100% = $2000

10% = $200

1% = $20

so, when there is a discount of 10%, then the corresponding $200 will be deducted from the price.

and the actual sales price of the couch is then

$2000 - $200 = $1800

little more practice to show the general thinking behind % :

let's say the discount is 18%. what now ?

well, we know how much 1% is. and we need then 18 times this 1% to deduct from the original price.

18% = 18 × 100%/100 or 100% × 18/100

so, for a couch of originally $2000 this is

18% = $2000 × 18/100 or $2000 × (1/100) × 18 or

($2000/100) × 18

whatever feels "nicer", but all of these approaches do the same thing and lead to the same result.

so, long story short :

18% = 18 × 1% = 18 × $20 = $360

and the sales price of the couch is then

$2000 - $360 = $1640

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: