From 2011 to 2012, Jack’s annual salary increased by 10 percent and Arnie’s annu

游客2025-02-24 9

问题 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 Amies annual salary in 2011 was what percent greater than Jack’s annual salary in 2011 ?
Give your answer to the nearest 0.1 percent.
______%

选项

答案 15.8

解析 Let k be Jack’s annual salary in 2011, and let r be Amies annual salary in 2011. Then Jack’s annual salary in 2012 was 1.1k, and Amies 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 =

k. Since

=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.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 5: Simplify an Arithmetic or Algebraic Representation

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