Understanding the Problem
Read the problem over and make sure you understand it. Pick out important information. The data I felt was important is in bold letters.
You haven't heard about the Great Gold Robbery? Well, in a way, it's not too surprising. The bankers at Fort Knox haven't been too anxious for the public to hear about the way all the money was taken out right from beneath their watchful eyes. Here's the way the story went, as I heard it:
Late one night a burglar somehow got into one of the vaults in the Fort and started out with a big sack of gold coins. No one really knows how much he stole. At any rate, on his way out, he was stopped by one of the guards who caught him "holding the bag", so to speak. Fortunately for him, the burglar was able to talk his way out of trouble by offering the guard half of the money he had taken with a bonus of $2,000 thrown in. Just as he was walking away, praising his good luck at having gotten free, he was stopped by a second guard. It took the same bribe, half of all the money he had left with $2,000 thrown in, to get by the second guard. Just as he was about to leave, you guessed it, he was stopped by yet a third guard who let him go only after receiving half of all the burglar had left, with $2,000 thrown in.
By the time the burglar left the front gate of Fort Knox, he had mixed emotions. After all, he did leave with $9,000 more than he had when he arrived and he escaped a free man. But as he thought of all the money he had left behind with the guards, he wept. Oh, by the way, you now know enough to calculate how much he had taken in the first place.
I felt the best method to solve this problem was to write and equation using the information provided.
We will call the amount of money x. It will be easiest to work backward starting with how much he had before the third guard until we get to how much he started with.
The equation for what he had before the third guard is: 1/2x - 2000
The equation for what he had before the second guard is: 1/2x - 2000
The equation for what he had before the first guard is: 1/2x - 2000
We also know that after the third guard he had $9000.
9000 = 1/2x - 2000
9000 + 2000 = 1/2x - 2000 + 2000
11000 = 1/2 x
11000 * 2 = 1/2x * 2
22000 = x
Before the first guard he had $22000
22000 = 1/2x - 2000
22000 + 2000 = 1/2x - 2000 + 2000
24000 = 1/2x
24000 * 2 = 1/2x * 2
48000 = x
Before the second guard he had $48000
48000 = 1/2x - 2000
48000 + 2000 = 1/2x - 2000 + 2000
50000 = 1/2x
50000 * 2 = 1/2x * 2
100000 = x
The robber started with $100,000
Now let's check our answer in the problem.
100000/2 - 2000 = 48000
48000/2 - 2000 = 22000
22000/2 - 2000 = 9000
Our answer is right.
S. A. Hudson: SHUDSON@nmu.edu.