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Directions: Your answer may be an integer, a decimal, or a fraction, and it may be negative. Enter the exact answer unless the question asks you to round your answer.
Q. From 2011 to 2012, Jack’s annual salary increased by 10 percent and Arnie’s annual salary decreased by 5 percent. If their annual salaries were equal in 2012, then Arnie’s annual salary in 2011 was what percent greater than Jack’s annual salary in 2011?
Give your answer to the nearest 0.1 percent.
Correct answer is '15.8'. Can you explain this answer?
Most Upvoted Answer
Directions: Your answer may be an integer, a decimal, or a fraction, ...


Understanding the Problem

To solve this problem, we need to compare Jack's and Arnie's annual salaries in 2011 and 2012. We are given that Jack's salary increased by 10% from 2011 to 2012, while Arnie's salary decreased by 5% over the same period. We are asked to find the percentage by which Arnie's salary in 2011 was greater than Jack's salary in 2011.

Calculating the Salaries

Let's assume Jack's salary in 2011 was J. After a 10% increase, his salary in 2012 would be 1.1J. Similarly, assuming Arnie's salary in 2011 was A, after a 5% decrease, his salary in 2012 would be 0.95A. Since their salaries were equal in 2012, we can set up the equation:

1.1J = 0.95A

Solving this equation, we get:

A = (1.1J) / 0.95

Finding the Percentage Difference

To find the percentage by which Arnie's salary in 2011 was greater than Jack's salary in 2011, we calculate:

((A - J) / J) * 100

Substitute the value of A from the above equation into this formula and simplify to get the percentage difference.

Final Answer

After performing the calculations, we find that Arnie's salary in 2011 was 15.8% greater than Jack's salary in 2011.
Free Test
Community Answer
Directions: Your answer may be an integer, a decimal, or a fraction, ...
Let k be Jack’s annual salary in 2011, and let r be Arnie’s annual salary in 2011. Then Jack’s annual salary in 2012 was 1.1k, and Arnie’s was 0.95r. Since their salaries in 2012
were equal to each other, you have 0.95r = 1.1k. Solving the equation for r, you get r = 1.1 / 0.95k. Since 1.1/0.95 = 1.1578…, it follows that, rounded to the nearest 0.1%, Arnie’s annual salary in 2011 was 15.8% greater than Jack’s annual salary in 2011. The correct answer is 15.8.
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Directions: Your answer may be an integer, a decimal, or a fraction, and it may be negative. Enter the exact answer unless the question asks you to round your answer.Q. From 2011 to 2012, Jack’s annual salary increased by 10 percent and Arnie’s annual salary decreased by 5 percent. If their annual salaries were equal in 2012, then Arnie’s annual salary in 2011 was what percent greater than Jack’s annual salary in 2011?Give your answer to the nearest 0.1 percent.Correct answer is '15.8'. Can you explain this answer?
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