Video Transcript
A shoe store is having a sale
in which all items are discounted 25 percent. Ethan paid 39 dollars, tax
included, for a pair of sneakers. If the sales tax is four
percent, how much did the pair of sneakers originally cost?
So, there are three key bits of
information here. The first is that the items are
all in a sale and they’re discounted 25 percent. The next is that Ethan paid 39
dollars. And then, finally, we’re told
the sales tax is four percent. The key thing to notice here is
that sales tax is put on at the end. So, it’s put on whatever value
or amount Ethan paid for the sneakers after the discount. So therefore, our first
calculation is to work out how much Ethan paid before the sales tax.
And what this is is something
called a reverse percentage because we have the final amount and we want to find
the original amount. And to solve reverse
percentages, we have a couple of methods we can use. The first method is to consider
the original amount and the final amount. Now, if we were to get to the
final amount from the original amount, and we’re looking at a percentage
increase or decrease, then all we would do is multiply by our multiplier.
So, therefore, if we wanted to
go the other way, so from our final amount to our original amount, then what we
would do is the converse of this. And we’d, in fact, divide by
our multiplier. So, that’s one method, or
model, that we can use. But there is another way of
thinking about reverse percentage. And this is the method, first
of all, that I’ll use to solve this problem. And that’s because it’s easier
to demonstrate when we have values.
Well, if we start by thinking
about the sales-tax part of the question, then our 39 dollars paid by Ethan is
equal to the total amount of the shoes before sales tax, which is 100 percent of
that amount, plus the four percent that the sales tax is. Well, therefore, we could think
of 39 dollars as 104 percent of the original amount that was paid after discount
but before sales tax.
So therefore, if we want to
find out what one percent is gonna be, we could divide this by 104, which will
be equal to 0.375 dollars. And then, to work out how much
the price after discount but before sales tax was, all we do is multiply this by
100 to get the 100 percent. Which will give us 37 dollars
and 50 cents. Okay, great, so this is the
first part of the question answered.
Well, now, for the second part
of the question so we can answer the question fully, what we’re gonna use is the
original method that we mentioned. And that is the
multipliers. Because if we got our original
amount, and that’s the amount after discount but before tax, then if we multiply
this by 0.75, we’ll get 37 dollars and 50. And we got that cause one minus
0.25 is 0.75. And that’s cause we’ve got a
discount of 25 percent. Then, if we wanna work
backwards, then what we’ll do is divide by 0.75. And when we divide 37 dollars
and 50 cents by 0.75, we get 50 dollars. So therefore, the original cost
is 50 dollars.
