A word of caution is in order here, because it would have been very easy to have made a
big mistake in Example 8.1.2. When using percents, we have to be careful what the percent
is of. The 65% markup used in this example was a percent of the cost, not of the selling
price. It is easy to overlook this and find the markup by multiplying by the selling price to
get (0.65)($7.95) $5.18, which is incorrect. In fact this would overstate the markup by
more than $2! It is vitally important to make sure that you are applying the percent to the
right thing when doing these sorts of calculations. These sorts of mistake not only lead to
lower marks on exams, but when used in the real world they have the potential to lead to
disastrously misguided business decisions.
If we know the cost and selling price, we can determine the percent markup from these,
as the next example will demonstrate.Example 8.1.3 An electronics retailer offers a computer for sale for $1,000. The
retailer’s cost is $700. What is the markup percent?Working from the formula, we get:P C(1 r)
$1,000 $700(1 r)Dividing both sides by $700 gives:1.4285714 1 rWe then subtract 1 from both sides and rewrite the result as a percent:r 0.4285714
r 42.86%You may observe that we could also have calculated this by noting that there is a $300
markup, and so as a percent of cost the markup is $300/$700 42.86%. This is also a
correct solution method.The same danger we saw in Example 8.1.2 is in play here. It is tempting to reason that the
dollar amount of the markup here is $300, and $300 is 30% of $1,000, and so wrongly
conclude that the markup is 30%. The same issue is at play: markup is a percent of cost,
not of selling price. Even though it is easy to see how someone could make this mistake
(especially when the selling price is a nice round number), doing so leads to a result that
misses the mark by quite a lot.
In the exercises you will have plenty of opportunity to work problems similar to these.
You may fi nd that you are able to fi nd the correct answers without relying too heavily on
the formula; if so, there is no need to rely on it too heavily. If you fi nd, though, that you
are making mistakes or getting confused, you may fi nd it helpful to slow down and work
things through carefully, and step by step, using the formula. When in doubt, slow down
and use the formula!Markdown
From ordinary life, we are all familiar with the idea of prices being
marked down, for example, as part of a sale or some other promotion.
Mathematically, markdown is quite similar to markup. To calculate
a marked-down price, we simply apply the percent the price is to be
marked down to the original price, and then subtract. For example, sup-
pose Eddie’s Bike World has a “10% off” sale on a bike that normally
sells for $352.50. 10% of $352.50 is (0.10)($352.50) $35.25, and so
subtracting off this discount gives us a sale price of $352.50 $35.25
Markdown in action! © PhotoLink/Getty Images/DIL $317.25.
334 Chapter 8 Mathematics of Pricing