Dear Tutors,
This question confuses me.
A book store is having a sale. All hardback books are 20% off, and all
paperbacks are 10% off. Suppose you buy four paperbacks that originally
cost $9 each and two hardbacks that originally cost $20 each. What
percent of the total cost have you saved? Round to the nearest percent.
This problem is badly worded. The red words "total cost" above could
either mean the "total cost" you ACTUALLY paid for all the books, or
they could mean the "total cost" you WOULD HAVE paid if the books had
not been on sale.
On each hardback you save 20% of $9, which is
.20($20) = $4
So on each of the hardbacks you save $4, so on
both hardbacks you save 2×$4 or $8
Each hardback originally sold for $20, and since $4 was
subtracted from the price of each, you pay $20 - $4 or
$16 for each hardback. Thus your total cost for the two
hardbacks is 2×$16 or $32.
On each paperback you save 10% of $9, which is
.10($9) = $.90 or 90 cents
So on each of the four paperbacks you save $.90, so on
the four paperbacks you save 4×$.90 or $3.60
Each paperback originally sold for $9, and since $.90 was
subtracted from the price of each, you pay $9.00 - $.90 or
$8.10 for each paperback. Thus your "total cost" for the
four paperbacks is 4×$8.10 or $32.40.
Your total savings is $8 saved on the hardbacks plus $3.60
saved on the papersbacks, or your total savings is
$8.00 + $3.60 or $11.60
Your "total cost" for all the books is $32 for the hardbacks
plus $32.40 for the paperbacks is $32.00 + $32.40 or $64.40
Now if those red words "total cost" means what you ACTUALLY
paid then the question we ask is:
What percent of $64.40 is $11.60?
So to find that we divide $11.60 by $64.40 and get .1801242236,
which is 18.01242236%, or rounded to hundredths is 18.01%.
Now if those red words "total cost" means what you WOULD HAVE
paid if the books had not been on sale then we must first
calculate what you WOULD HAVE paid if they had not been on
sale. That would have been $20×2 or $40 for the hardbacks
plus $9×4 or $36 for the paperbackas. That's a total of
$40+$36 or $76
Now the question we would ask is:
What percent of $76 is $11.60?
So to find that we divide $11.60 by $76 and get .1526315789,
which is 15.26315789%, or rounded to hundredths is 15.26%.
Sorry I can't tell which the red words mean. Be sure to
ask your teacher.
Edwin