A library expansion, begun in 2002, was expected to cost $107 million. By 2006, library officials estimate the cost would be $32 million over budget. By what percent did the actual cost exceed the initial estimate?

Question

anonymous · Answer

I need major help!! I have tried and tried to understand this problem and I just cant seem to get it!!

anonymous · Answer

Maybe easier numbers would help you get the idea...

Say you buy a meal for $10.  Next time, you buy a meal for $15.  By what percent did your second meal price increase over your first meal price?

It increased by $5, right?   You compare the new price $15 to the old price $10, and subtract to see that the price increased by $5.

Then divide that price difference by the original price to get the percentage increase...
5/10 = 50% increase.

Percent increase = (new amount - old amount) / (old amount)

anonymous · Answer

ok, I see it..  So since the question is saying the budget went over would I add the 32 million to the 107 million to get 139 million instead of subtracting? Or am I wrong?

anonymous · Answer

well, you confused yourself just a bit, but you're on the right track :)

new amount = 32 + 107 = 139  since the problem said it would be over budget by $32 million.

However, when you do "new - old", you get 139 - 107 = 32

So the percentage change is (139 - 107)/107

you could have just used 32/107 and gotten the same result.

anonymous · Answer

Oh I see, so where I was confusing myself was just the subtraction.. Ok, I think I get it you explained it very well. Thank you very much for your help!

anonymous · Answer

Now i just had to round my answer to the nearest tenth and I did get the correct answer finally! Thanks so much!

anonymous · Answer

great!  glad to help :)