College Algebra with Modeling & Visualization (6th Edition)
College Algebra with Modeling & Visualization (6th Edition)
6th Edition
ISBN: 9780134418049
Author: Gary K. Rockswold
Publisher: PEARSON
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Chapter D, Problem 1E
To determine

For the given amount A and B , find:

  (a) The percent change if A changes to B.

  (b) The percent change if B changes to A.

Expert Solution & Answer
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Answer to Problem 1E

Solution:

  (a) The percent change if A changes to B is 100%_ .

  (b) The percent change if B changes to A is 50%_ .

Explanation of Solution

Given:

  A=$500,  B=$1000 .

Formula Used:

Percentage change: When an amount A1 changes to a new amount A2 , then the percent change is given by:

  A2A1A1×100%

Calculation:

  (a) Using the formula for percentage change, we can write the percentage change when A changes to B as shown below.

  BAA×100%

Now, we plug in the values of A and B in the above formula and simplify it to get the value in percentage form.

  BAA×100%=1000500500×100% =500500×100%(Subtract: 1000500=500) =50000500%(Multiply: 500×100=50000) =100%

Thus, the percent change if A changes to B is 100% .

  (b) Now similarly when B changes to A , the percent change formula becomes

  ABB×100%

Now, we plug in the values of A and B in the above formula and simplify it to get the value in percentage form.

  ABB×100%=50010001000×100% =5001000×100%(Subtract: 5001000=500) =500001000%(Multiply: 500×100=50000) =50%

Thus, the percent change if B changes to A is 50% .

Conclusion:

The percent change if A changes to B is 100% , and the percent change if B changes to A is 50% .

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