Answer:
Part a) The new price is ![\$400](https://tex.z-dn.net/?f=%5C%24400)
Part b) The percent decrease is 20%
Part c) The percent decrease is 9.375%
Step-by-step explanation:
we know that
The original price of a sofa is $500
This price represent the 100%
Part a) If the sofa price decreased by 20%, what is the new price?
Let
x -----> the new price
we know that
![100\%-20\%=80\%=80/100=0.80](https://tex.z-dn.net/?f=100%5C%25-20%5C%25%3D80%5C%25%3D80%2F100%3D0.80)
so
The new price is equal to the original price multiplied by 0.80
![x=500(0.80)=\$400](https://tex.z-dn.net/?f=x%3D500%280.80%29%3D%5C%24400)
Part b) The company can’t sell the sofa after 3 weeks so they reduce the price to $320. What is the percent decrease?
In this moment the price of sofa is $400
Find the difference between the original price and the new price
![\$400-\$320=\$80](https://tex.z-dn.net/?f=%5C%24400-%5C%24320%3D%5C%2480)
using proportion
Find out the percent decrease
Let
x ----> the percent decrease
![\frac{400}{100}=\frac{80}{x}\\\\x=100*80/400\\\\x=20\%](https://tex.z-dn.net/?f=%5Cfrac%7B400%7D%7B100%7D%3D%5Cfrac%7B80%7D%7Bx%7D%5C%5C%5C%5Cx%3D100%2A80%2F400%5C%5C%5C%5Cx%3D20%5C%25)
Part c) If the company reduces the price in week 4 to $290, what is the percent decrease?
In this moment the price of sofa is $320
Find the difference between the original price and the new price
using proportion
Find out the percent decrease
Let
x ----> the percent decrease
![\frac{320}{100}=\frac{30}{x}\\\\x=100*30/320\\\\x=9.375\%](https://tex.z-dn.net/?f=%5Cfrac%7B320%7D%7B100%7D%3D%5Cfrac%7B30%7D%7Bx%7D%5C%5C%5C%5Cx%3D100%2A30%2F320%5C%5C%5C%5Cx%3D9.375%5C%25)