Bank Robbery

Obsidantion · #1 $Old$ 10-20-2008, 03:31 PM

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?

Soroban · #2 $Old$ 10-20-2008, 09:06 PM

Hello, Obsidantion!

Quote:

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!

Obsidantion · #3 $Old$ 10-21-2008, 06:58 AM

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.