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Budget overruns. The massive roadworks project in Boston known as The Big Dig cost approximately $14.6 billion. This cost was 484% more than the original estimate. What was the original estimate of the cost of The Big Dig?

Question

mertsj · Answer

Let x = original cost
4.84x = 14.6 billion
4.84x/4.84 = 14.6/4.84
x = 3.02 billion

whpalmer4 · Answer

That's close, but incorrect :-)  The key is that the cost was 484% more than the original estimate, which is not the same as 484% of the original estimate.    Original estimate*(1+percentage more/100) = Final
You can see this to be true if you consider some obvious percentages: if the cost is 0% more than the original estimate, the formula reduces to original*(1+0/100) = original; if the cost is 100% more than the original estimate, you get original*(1+100/100) = 2 * original.

so, in this case, x = original cost.  final cost=(1+484/100)*original or $14.6 billion = (1+4.84)*x and so x = $14.6 billion / 5.84 = $2.5 billion

The numbers I've seen say the original estimate was $2.6 billion, not 2.5, but what's $10^8 between friends? :-)

anonymous · Answer

Let x be the original estimate.  Solve the following for x:$$100\%x+484\% x \text{=} 14.6*10^9$$$$1.00x+4.84 x = 14.6*10^9$$$$x+4.84 x = 14.6*10^9 $$$$x=2.5\times 10^9 $$The above was solved with the aid of Mathematica.

I don't want to ruffle any feathers here, but in some circles, "between friends" would be read, between democrats when it comes to that project.