I can't figure out how to solve this problem

Question

a library expansion began in 2002, was expected to cost 101 million. By 2006, library officials estimate the cost would be over budget by 36 million. By what percent did the actual cost exceed the initial estimate? I can't figure out how to go at this problem at it first I thought about dividing the two but that didn't get me anywhere. Can you please help?

Answer 1

Hi, Cynthia! You might have done this correctly - maybe you should have more trust in your instincts - but let's go through it together.

 

Consiser the facts before us:

1. The initial cost estimate was $101 million. I believe we are expected to assume this was the amount budgeted for the project;

2. The actual cost of construction exceeded the original estimate by $36 million. This means the actual cost came out to $137 million.

 

So, $36 million is the amount that exceeded the budget of $101 million. You simply need to find out what portion or percentage of 101 is 36. Make sense?

 

Make a fraction: 36/101

 

Did you divide 36 by 101? If so you were correct!

 

Use your estimation skills & think of it this way:

 

101 is very close to 100, which is the basis for percentages, so let's round it to 100. 36/100 would be 36%, so the project exceeded budget by about 36%. Now, divide 36 by 101. Is it pretty close to 36% (should be 35.64...%). It's less than 36% because 101 goes into 36 fewer times than does 100.

 

I hope this helps you better understand percentages!