Plez send help

[xX_mathlordXx_98]

The price of an article first increases by 10%; thereafter the price decreases by 20%. What is the percentual change? For a decrease use the negative sign (-). Round your answer to two decimal places and use a decimal point.

??? I tried with 10% cause I thought that makes the most sense but apparently not!

The price of an article is € 14.17. This price is the result of a decrease of the original price by 3.5%. What was the original price? Round your answer to two decimal places and use a decimal point.

 

[lev888]

Please post one problem per thread.
What exactly did you try with 10%?

 

[Deleted member 4993]

Suppose a material goes on sale with 20% reduction. The original price was $ 110. What is the "sale price" after 20% reduction?

 

[HallsofIvy]

The price of an article first increases by 10%; thereafter the price decreases by 20%. What is the percentual change? For a decrease use the negative sign (-). Round your answer to two decimal places and use a decimal point.

If the original price is P, after the increase the price will be P+ 0.10P= 1.10P. After the decrease it will be 1.10P- (0.2)(1.10P)= 1.10P- (0.3)(1.10)P= 1.10P- 0.33P= (1.1- 0.33)P= 0.77P. 1- 0.77= 0.23 so this is a -23% change. (It seems strange that you are told to "round your answer to two decimal places and use a decimal point" when the answer is to be given as a percent. If you were not told to write the answer as a percent, it would be a -0.23 change which requires two decimal places (but still no "rounding". Perhaps they want 23.00%?)

??? I tried with 10% cause I thought that makes the most sense but apparently not!

The price of an article is € 14.17. This price is the result of a decrease of the original price by 3.5%. What was the original price? Round your answer to two decimal places and use a decimal point.

Let the original price be "P". A decrease in the original price would be a decrease of 0.035P so the new price is P- 0.035P= (1- 0.035)P= 0.965P= 14.17. Can you solve that for P?

 

[Steven G]

HallsofIvy had a typo in his work above. Somehow (0.2) became (0.3) so I will work it out (hopefully) correctly
Let P be the original price.
The price goes up 10%. So the new price P = original price + the extra 10% of the original price = P + .10P = 1P + .01P = (1.01)P
Now the 1.01P price is reduced by 20%
There are two ways to proceed from here.

1st method: If the price is reduced by 20%, then you are paying 80% of the price. So we need to calculate 80% of 1.01P = .8*1.01P= .808P= 80.8% The percent change is -19.2%

Method 2: The price goes down 20%. So the new price will be the price you are taking off 20% from - 20% of that price.
1.10P - .20(1.01)P = 1(1.10P) - .20(1.01P) = .80(1.01P) = .808P = 80.8% of P.


Since 10% and 20% are somewhat small percentages I can see how you might think that the answer is -10%
So lets look at another example. Suppose an item cost $100 and then the price increases by 50% and then decreases by 50%
Now $100 + a 50% increase will be $100 + $50 = $150. Now we reduce the item by 50% which is by 1/2. 50% or 1/2 of $150 is $75. So the new price will be $150-$75=$75 NOT $100. You just can't do 50%-50% = 0% so there is no change in price! So what is going on? Well if you take 50% (or any % =0%) of different amounts you will get different answers! 1st we took 50% of $100 and then 50% of $150. That is we added (50% of $100) to $100 and then took away 50% of that sum. That is what we 1st added to $100 (namely $50) was NOT what we then took away from $150 (namely $75). Think about this!