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Math Help - Bank Robbery

  1. #1
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    Bank Robbery

    Two bank robbers, Ron and Jon, have managed to steal 42 crates of gold and silver bars from a bank, 392 of the bars they stole being gold.

    Of the 42 crates, there are only two distinctive types regarding the amount and total worth of the bars that each crate contains. One type of crate contains 11 bars and is worth 140k, the other contains 20 bars and is worth 280k.

    Jon, being the brains behind the operation, was elected to calculate how the takings would be divided between him and Ron and decided that he would take all of the crates that contained 20 bars and are worth 280k and leave the rest to Ron.

    Ron isn't very happy that he's been left with the crates that are individually half as valuable as Jon's. Given that each gold bar is worth 15k and each silver bar is worth 10k, can you help Ron work out how much money in material value Jon has deviously given himself more than he has Ron?
    Last edited by Obsidantion; October 20th 2008 at 01:58 PM.
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  2. #2
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    Hello, Obsidantion!

    Two bank robbers, Ron and Jon, have managed to steal 42 crates
    of gold and silver bars from a bank, 392 of the bars they stole being gold.

    Among the 42 crates, there are two distinctive types.
    One type of crate contains 11 bars and is worth $140k,
    the other contains 20 bars and is worth $280k.

    Jon was elected to calculate how the takings would be divided between them,
    and decided that he would take all of the crates that contained 20 bars
    and leave the rest to Ron.
    Ron is unhappy that he's left the crates worth half as much Jon's.

    Given that each gold bar is worth $15k and each silver bar is worth $10k,
    work out how much Jon has given himself more than he has Ron?

    Small crates: 11 bars worth $140k

    Let x = number of gold bars.
    Let 11-x = number of silver bars.

    x gold bars at $15k each are worth: . 15kx dollars.
    11-x silver bars at $10k each are worth: . 10k(11-x) dollars.

    Total value is $140k: . 15kx + 10k(11-x) \:=\:140k

    Solve for x\!:\;\;x \:= \:6 \quad\Rightarrow\quad 11-x \:= \:5

    \boxed{\text{Small crate: }\begin{array}{c}\text{6 gold bars} \\ \text{5 silver bars} \end{array}}


    Large crates: 20 bars worth $280k

    Let x = number of gold bars.
    Let 20-x = number of silver bars.

    x gold bars at $15k each are worth: . 15kx dollars.
    20-x silver bars at $10k each are worth: . 10k(20-x) dollars.

    Total value is $280k: . 15kx + 10k(20-x) \:=\:280k

    Solve for x\!:\;\;x \:=\:16\quad\Rightarrow\quad 20-x :=\:4

    \boxed{\text{Large crate: }\begin{array}{c}\text{16 gold bars} \\ \text{4 silver bars} \end{array}}


    Let S = number of small crates.
    Then 42-S = number of large crates.

    S small crates with 6 gold bars each: . 6S golds bars.
    42-S large crates with 16 gold bars each: . 16(42-S) gold bars.

    Total gold bars is 392: . 6S + 16(42-S) \:=\:392

    Solve for S\!:\;\;S \:=\:28 \quad\Rightarrow\quad 42-S \:=\:14

    Hence: . \boxed{\begin{array}{c}\text{28 small crates}\\ \text{14 large crates} \end{array}}


    Jon took the 14 large crates worth $280k each.
    . . His share is: . 14 \times \$280k \:=\:\$3920k

    Ron took the 28 small creates worth $140k each.
    . . His share is: . 28 \times \$140k \:=\:\$3920k


    They shared the loot equally!

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  3. #3
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    Quote Originally Posted by Soroban View Post


    They shared the loot equally!

    So Jon was an alrigh' guy after all... except for the taking of people's money.

    Well done Soroban! If intelligence was a crime, you would be a master criminal.
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