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Last year the price of a pen was $9.98.
This year the price of a pen increased by 15%.
During the Christmas sale the price of the pen was reduced by 20 percent from this
year's price.
What is the price of the pen during the Christmas sale? So we have a few
increases and decreases or
a few change of percentages here. So we just want to keep tracking going in
chronological order, so I'll start with last year.
The price at the pen was nine dollars and ninety eight cents.
This year the
pen increased by 15 percent. So one
way we can do this is to multiply this times
15 percent and then we want to add this
back to their original amount and this will get you
$11.477.
We'll worry about rounding later.
Then it says that during a Christmas sale
the price of the pen was reduced by
20 percent, so we'll say that Christmas sale , the original price
is eleven dollars and
roughly 48 cents. Now where decreasing this
amount by 20 percent, so
this will be the original amount.
Subtract 20 percent of that original
amount and this gives you $9.1816.
So at this point we can round our answer to nine
dollars and eight cents.
Now one thing I want to mention which I think is pretty...
it's helpful, because it increases your efficiency with these types of questions,
instead of having to do these additions and subtractions
let's re-write this year's
and the Christmas sale price. Instead of taking fifteen percent
of the original number and then having to re-add it to the original amount,
let's do that in one clean
step. If we multiply nine dollars and ninety eight cents
and multiply times a 115 percent of
the price, that accounts for the original plus
15 percent, right? And you'll find that if you type that into your calculator, you get exactly the same
thing.
This is when we increase
the price, and so obviously it's going to be more than a hundred percent of the original
price.
now for a decrease in price, in this case a 20 percent decrease,
we want to think about how much of the original
100 percent is actually being payed for. If we're at a discount of 20 percent,
it's kind of the same thing as saying
we're only paying eighty percent of their original cost. Again if you do 11.477
times .80, you'll get
9.1816, which is
again the same answer. So again try practicing this.
We want to be multiplying times, in a way, kind of the opposite
percentage, where I just mean a hundred minus whatever
percent. If you are decreasing a hundred
plus the percent as a decimal if you're increasing.