# Don't Get It!!!!

• Oct 23rd 2006, 07:49 AM
frogsrcool
Don't Get It!!!!
At a a local grocery store, the bananas they recieve are transported through three stages: from the farmer to the market, market to the wholsaler, and from the wholsaler to the grocery store. At eachstage, the price of the banannas increase by 20% of the previos price. If a person buys 80cents worth of bannas at the grocery store, how much was the farmer paid for thos bananas?

How would I do this question? :confused: :confused:
• Oct 23rd 2006, 09:26 AM
Soroban
Hello, frogsrcool!

I'll use a head-on approach . . .

Quote:

At a a local grocery store, the bananas they receive go through three stages:
from the farmer to the market, market to the wholsaler,
and from the wholsaler to the grocery store.
At each stage, the price of the bananas increase by 20% of the previous price.
If a person buys 80cents worth of bannas at the grocery store,
how much was the farmer paid for those bananas?

The farmer was paid $\displaystyle x$ cents for those bananas.

The market raised the price by 20%.
. . That is: .$\displaystyle 120\%\text{ of }x\;=\;1.2x$ cents.
And sold them to the wholesaler for $\displaystyle 1.2x$ cents.

The wholesaler raised the price by 20%.
. . That is: .$\displaystyle 120\%\text{ of }1.2x\;=\;1.44x$ cents.
And sold them to the grocery store for $\displaystyle 1.44x$ cents.

The grocery store raised the price by 20%.
. . That is: .$\displaystyle 120\%\text{ of }1.44x \;= \;1.728x$ cents.
And sold them to the customer for $\displaystyle 1.728x$ cents.

We are told that the customer paid $\displaystyle 80$ cents for the bananas.

Hence, we have: .$\displaystyle 1.728x \:=\:80\quad\Rightarrow\quad x \:=\:\frac{80}{1.728} \:=\:46.2962963$

Therefore, the farmer was paid about 46.3¢ for the bananas.

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Check: .$\displaystyle 46.3 \times 1.2 \times 1.2 \times 1.2 \:= \:80.0064$ . . . Yes!