How Does a 30% Price Increase Affect Sales to Result in a 9% Revenue Decrease?

[kiranmayi]

when the price of a box of peanuts is increased by 30% its sales decreased by x% such that the revenue decreased by 9%.what is the value of x?
solution:
let cost price=100 ,
with an increase of 30%selling price is 130, revenue is 9% lessso he incurred a loss of 9% over the income he has to get by selling x number of articles.so...
pls help me homework to solve it.just got stuck here

 

[zzephod]

Let the original price be \(\displaystyle P_0\), the original sales be \(\displaystyle X_0\) and the original revenue be \(\displaystyle R_0\).

Then \(\displaystyle R_0=X_0 P_0\). Now the price is increased to \(\displaystyle P_1=1.30 P_0\), and sales become \(\displaystyle X_1=\left(1-\frac{x}{100}\right)X_0\) and revenue \(\displaystyle R_1=0.91 R_0\).

We also have:

\(\displaystyle R_1=X_1P_1\)

Substituting in from the previous paragraph we get:

\(\displaystyle 0.91R_0 = \left( 1-\frac{x}{100}\right) X_0 \times 1.30 P_0=\left( 1-\frac{x}{100}\right) \times 1.30 R_0\)

from which you can solve for \(\displaystyle x\).