I find that it's useful to keep a few simple examples in my head. (The new value is 300% of the old value.) Doctor Ian didn’t mention it, but their misreading of the problem may very well have been due to the thinking discussed in this post: Three Times Larger: Idiom or Error? Let's put the two cases together, so you can compare them more easily:ġ) Claims in 2001 are an increase of 300% over claims in 1999.Ģ) Claims in 2001 are 300% of the claims in 1999. That is, if the new is just 300% of the old (3 times as much), we just divide by 3. That is, if we say that the number of claims in 2001 is 300% of the number of claims in 1999, then we're saying So how did the others get their answer? They were missing the word “increase”: Note that if we change the wording slightly, we can come up with the other answer. So the number of claims in 2001 is 4 times whatever it was in 1999, which means there were 2,500 claims in 1999.Īnother way to say this would be that a 300% increase means that the new value is 100% + 300% = 400% of the original (that is, 4 times the original) so to get back to the original, we divide by 4. Since the numbers are so nice and round, we can do this: That is, we're saying that the _increase_ is 300% of the original value. (We’ll be looking at that soon!) Doctor Ian replied: A 300% increase means that Very likely the large percentage was part of the reason for the dispute, as it can confuse people. My colleagues are giving me all different answers. If there were 10,000 claims in 2001, and that is a 300 percent increase since 1999, how many claims were there in 1999? Here’s a 2003 question that focused on distinguishing what we’ve been doing here from a straight percentage calculation: Percentage Increase vs. It could also have been calculated as 2/102. So if p is 2 percent, q would beĪnd this q turns out to be 0.0196078…, which rounds to Elias’ 1.96%. If we increase something by 1/3, we should have to decrease it by 1/4: If we increase something by 100%, we should have to decrease it by 50% to get back to where we started: Turning these into formulas, we can reverse a P% decrease using $$\text.$$ Let's check this with a simple example. We could instead have merely divided separately by each multiplier (1.07 and 0.80) to get the answer. To undo this, we just divide by the multiplier. What he has done here is first to combine the two changes (7% increase and 20% decrease) by multiplying 107% and 80% to get a net multiplier of 85.6%. The 107% is similar (but unnamed, to my knowledge): It represents what percentage the new value is of the old value. Recall from last time that 80% is called the complement of the 20% decrease, and represents the remaining percentage. And since the word "of" means "times" in percent problems, we get If x is the original price, then we are paying 107 percent of (the sale price), which is 107 percent of (80 percent of the original price). We'll use these two ideas in the problem. When 7 percent tax is added to a price, you have to pay that plus 100 percent of what you normally would, for a total of 107 percent of the actual price. So this question covers both.ĭoctor Brian answered: When 20 percent is discounted from a price, you still have to pay 80 percent of the original price. Here we have to back off both a tax (which amounts to a percent increase) and a discount (a percent decrease). What was the list price of the calculator, without tax, before discount? After adding 7 percent tax, the total cost is $20.07. We can start with this question from 1996: Price before DiscountĪ calculator is discounted 20 percent. Having discussed how to calculate the percent change between two numbers, and how to apply such a change to one number to get a new number, we need to look at what may be one of the most common types of questions we get: reversing a percent change (increase or decrease) to find the original value.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |