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Math Help - Don't Get It!!!!

  1. #1
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    Unhappy 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?
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, frogsrcool!

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


    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 x cents for those bananas.

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

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

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

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

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


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

    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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

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