SATII数学考试考题快递—Common Word Problems(II)

Price

In rate questions dealing with price, you will usually find the first quantity measured in numbers of items, the second measured in price, and the rate in price per item. Let’s say you had 8 basketballs, and you knew that each basketball cost $25 each:

Percent Change

In percent-change questions, you will need to determine how a percent increase or decrease affects the values given in the question. Sometimes you will be given the percent change, and you will have to find either the original value or new value. Other times, you will be given one of the values and be asked to find the percent change. Take a look at this sample problem:


	A professional golfer usually has an average score of 72, but he recently went through a major slump. His new average is 20 percent worse (higher) than it used to be. What is his new average?

This is a percent-change question in which you need to find how the original value is affected by a percent increase. First, to answer this question, you should multiply 72 by .20 to see what the change in score was:

Once you know the score change, then you should add it to his original average, since his new average is higher than it used to be:

It is also possible to solve this problem by multiplying the golfer’s original score by 1.2. Since you know that the golfer’s score went up by twenty percent over his original score, you know that his new score is 120% higher than his old score. If you see this immediately, you can skip a step and multiply 72

1.2 = 86.4.

Here’s another example of a percent-change problem:


	A shirt whose original price was 20 dollars has now been put on sale for 14 dollars. By what percentage did its price drop?

In this case, you have the original price and the sale price and need to determine the percent decrease. All you need to do is divide the amount by which the quantity changed by the original quantity. In this case, the shirt’s price was reduced by 20 – 14 = 6 dollars. So, 6

20 = .3, a 30% drop in the price of the shirt.

Double Percent Change

A slightly trickier version of the percent-change question asks you to determine the cumulative effect of two percent changes in the same problem. For example:


	A bike has an original price of 300 dollars. Its price is reduced by 30%. Then, two weeks later, its price is reduced by an additional 20%. What is the final sale price of the bike?

One might be tempted to say that the bike’s price is discounted 30% + 20% = 50% from its original price, but the key to solving double percent-change questions is to realize that each percentage change is dependent on the last. For example, in the problem we just looked at, the second percent decrease is 20 percent of a new, lower price—not the original amount. Let’s work through the problem carefully and see. After the first sale, the price of the bike drops 30 percent:

The second reduction in price knocks off an additional 20 percent of the sale price, not the original price:

The trickiest of the tricky percentage problems go a little something like this:


	A computer has a price of 1400 dollars. Its price is raised 20%, and then lowered 20%. What is the final selling price of the computer?

If this question sounds too simple to be true; it probably is. The final price is not the same as the original. Why? Because after the price was increased by 20 percent, the reduction in price was a reduction of 20 percent of a new, higher price. Therefore, the final price will be lower than the original. Watch and learn: