Question

Late one night a burglar got into one of the vaults in Fort Knox and he stole a big sack of gold coins. On his way out, he was stopped by one of the guards who saw him stealing the bag . Fortunately for him, the burglar was able to negotiate a deal with the guard and offered him half the money he had taken, plus an extra $2,000 thrown in. Just as he was walking away, thinking he had gotten away he was stopped by a second guard who took the same bribe: Half the money with an extra $2000 thrown in. Just as he was about to leave , he was stopped by a third guard who let him go only after receiving half of all the burglar had left with $ 2,000 extra thrown in. By the time he left he had mixed emotions. After all he did leave with $9,000 more than he had when he arrived and he was able to escape. But he thought of all the money he left behind. How much did he steal in the first place?

Answer 1

We can start by using algebra to represent the information given in the problem. Let x be the amount of money the burglar stole initially.

According to the problem, when the burglar gave half of the money plus $2,000 to the first guard, he was left with x/2 + 2000.

When he gave the same amount to the second guard, he was left with (x/2 + 2000)/2 + 2000.

And when he gave the same amount to the third guard, he was left with ((x/2 + 2000)/2 + 2000)/2 + 2000.

But we know that he left with $9,000 more than he had when he arrived, So we can say:

((x/2 + 2000)/2 + 2000)/2 + 2000 = x + 9000

We can now solve for x:

x = (900022*2 - 6000)/3

x = 36000/3

x = 12000

So the burglar stole $12000 in the first place.