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Math Help - Constructing Linear Equations

  1. #1
    Junior Member 22upon7's Avatar
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    Constructing Linear Equations

    Can someone please explain how you work this sum out, preferrably step by step?

    A shopkeeper buys a crate of eggs at $1.50 per dozen. He buys another crate, containing 3 dozen more than the first crate, at $2.00 per dozen. He sells all for $2.50 a dozen and makes $15 profit. How many dozens were there in each of the crates?
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by 22upon7 View Post
    Can someone please explain how you work this sum out, preferrably step by step?

    A shopkeeper buys a crate of eggs at $1.50 per dozen. He buys another crate, containing 3 dozen more than the first crate, at $2.00 per dozen. He sells all for $2.50 a dozen and makes $15 profit. How many dozens were there in each of the crates?
    Let there be x dozens in the first crate

    then dozens in the second crate=......

    amount of purchase=dozen*buying price per dozen

    selling amount=dozen*selling price per dozen

    profit=selling amount- purchasing amount

    Spoiler:

    dozens in second crate=x+3

    cost of purchase= x.$1.5 +(x+3).$2

    selling amount=(2x+3).$2.5

    profit($15)=(2x+3).$2.5-[x.$1.5 +(x+3).$2]

    which gives x=9

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