知识点地图 / 问题解决与数据分析
Percent Change, Discounts & Successive Change
百分率增减・折扣与复合变化
先问“以谁为基数”，再把百分率变成倍率。连续变化用乘法，反求原量用除法。
这部分需要会什么？
- 用乘数表示增加、减少与折扣
- 计算连续变化后的净变化率
- 根据变化后的数量反求原数
核心概念与公式
增加 \(r\%\) 对应乘 \(1+r/100\)，减少 \(r\%\) 对应乘 \(1-r/100\)。连续变化的总乘数是各步乘数的乘积，不能简单把各百分率相加。
变化率等于 \((\text{新值}-\text{原值})/\text{原值}\)。若已知新值，要用新值除以总乘数反求原值。百分率之间的绝对差用“百分点”描述；从 20% 到 30% 是增加 10 个百分点，相对原百分率增加 50%。
做题时怎样使用
- 每一步都明确本次以哪个量为基准
- 把文字增减转成乘数，再相乘
- 净变化看总乘数与 1 的差，反求原数则做除法
容易混淆的地方
先涨 20% 再降 20% 不会回到原值，因为第二次以涨价后的数为基准。降价后的价格不能直接再减同一比例来求原价。
用一个例题串起方法
知识点教学例题一件商品原价 200 元，先涨价 20%，再降价 20%。求最终价格与净变化率。
展开解题思路 ＋
最终价格为 \(200\times1.2\times0.8=192\) 元。总乘数为 0.96，所以相对原价下降了 \(4\%\)。
本知识点题库
先独立作答，再查看答案与解析。
百分率增减・折扣与复合变化进阶
In 2013, Chloe earned 11% more than in 2012, and in 2014 Chloe earned 6% more than in 2013. If Chloe earned y times as much in 2012 as in 2014, which of the following is closest to the value of y?
知序中文精讲
百分率增减・折扣与复合变化进阶
In 2007, Elijah earned 17% more than in 2006, and in 2008 Elijah earned 3% more than in 2007. If Elijah earned y times as much in 2006 as in 2008, which of the following is closest to the value of y?
知序中文精讲
百分率增减・折扣与复合变化进阶
The population of City A increased by 9% from 2015 to 2016.If the 2016 population is k times the 2015 population, what is the value of k?
原库参考解析
百分率增减・折扣与复合变化进阶
A scientist studying the life cycle of butterflies counted the number of butterflies in a certain habitat each day for 46 days. On June 15, there were 152 butterflies in the habitat. The percent increase in the number of butterflies in the habitat from May 1 to June 15 was 18.75%. How many butterflies were in the habitat on May 1?
原库参考解析
百分率增减・折扣与复合变化挑战
A scientist studying the life cycle of butterflies counted the number of butterflies in a certain habitat each day for 46 days. On June 15, there were 126 butterflies in the habitat. The percent increase in the number of butterflies in the habitat from May 1 to June 15 was 31.25%. How many butterflies were in the habitat on May 1?
原库参考解析
百分率增减・折扣与复合变化挑战
A clothing store buys shirts at a wholesale price of 4.00 dollars each and resells them each at a retail price that is 340% of the wholesale price. At the end of the season, any remaining shirts are marked at a discounted price that is 80% off the retail price. What is the discounted price of each remaining shirt, in dollars?
原库参考解析
百分率增减・折扣与复合变化挑战
The value of an autographed baseball increased by 178% from the end of 2012 to the end of 2013 and then decreased by 21% from the end of 2013 to the end of 2014. What was the net percentage increase in the value of the autographed baseball from the end of 2012 to the end of 2014?
原库参考解析
百分率增减・折扣与复合变化进阶
The expression 0.33x represents the result of decreasing a positive quantity x by what percent?
原库参考解析
百分率增减・折扣与复合变化挑战
The expression kx represents the result of decreasing a positive force, x, acting on an object by 0.34%. What is the value of k?
原库参考解析
百分率增减・折扣与复合变化挑战
A gallery had x artifacts in a collection. When more artifacts were added to the collection, the number of artifacts increased by 149%. What is the resulting number of artifacts in the collection in terms of x?
原库参考解析
百分率增减・折扣与复合变化挑战
The result of increasing the quantity x by 800% is 504. What is the value of x?
原库参考解析
百分率增减・折扣与复合变化进阶
The price of an object increased from $16 to $80. What was the percent increase in the price of the object?
原库参考解析
