Hints and solutions to Guess and Check #7
A Super Notebook was on sale last week
at
15% off the regular
price. Then an additional 10% of the sale price was deducted to give
a final super sale price of $25.09. What was the regular price of
the notebook?
- We could do this by guessing - for instance, suppose the original
price
was $30. After the store took 15% off, the price would have been
30 - 0.15(30) = 30 - 4.50 = 25.50. Then after the additional 10 % is
taken
off this price it would be 25.50 - 0.10(25.50) = 25.50 - 2.55 = 22.95.
This is too low, so we need to revise our guess higher.
-
Or, we could work backwards again. If the price ended up as $25.09
after
a 10% discount, then the price must have been 25.09/0.90 = 27.88 before
the
second discount. Before the first discount of 15%, then, the price must
have
been 27.88/0.85 = $32.80.
-
We can check this answer by working back again: Starting from
$32.80, a 15%
discount takes 0.15(32.80) = 4.92 off the price, leaving $27.88, and then
an
additional 10% discount takes 2.79 off the discounted price, for $25.09,
as it
should be.
-
A more algebraic approach would let p be the original price.
Then we must solve 0.9(0.85)p=25.09. In other words, we need to
solve 0.765p = 25.09. Therefore p = 25.09/0.765 = $32.80 as
before.