Hints and solutions to Guess and Check #2
Mary visited the Cherry Hill Mall. She bought a scarf for $5.00, spent
1/2 of her remaining money on
jogging shoes, bought lunch for $2.00 , then spent 1/2 of her remaining
money on a CD. She had $10.00 left. How much did she start with? (Also,
how much did the jogging shoes and the CD cost?)
- As for yesterday's problem,
there are multiple approaches to this: a guess and check approach,
a "work-backwards" approach (this would be nice to talk through so that
students see the advantage of working back from an answer!), and an
algebra approach.
-
The guess and check approach: Just guess how much money Mary had to begin
with. Say she started with $50. Then after the scarf she would have $45,
then she would spend $22.50 on the jogging shoes, leaving her with
$22.50. After $2 for lunch, she's down to $20.50. She will spend half of
this on the CD, leaving her with $10.25 - so our guess was pretty close,
and just a little high. Adjust, and try again.
-
The work-back approach starts with the $10 and says - "this is half of
the money Mary had before she bought the CD - so she had $20 before the
CD". Then "un-buying" lunch gives her $22, which is half of what she had
before the jogging shoes. So she had $44 before the shoes, then add the
$5 for the scarf to see that she had $49 to begin with. And along the
way, we discovered that the CD cost $10 and the shoes cost $22.
-
The algebra approach isn't so different - if x is how many dollars Mary
started with, then the operations she did on her pocketbook amount to:
((x-5)*1/2-2)*1/2 (here, * means "multiply"). This leaves her with $10,
so we have the equation
((x-5)/2 - 2)/2 = 10, which simplifies to (x-5)/2 - 2 = 20, then to
(x-5)/2 = 22, then to
(x-5)=44, and finally x=49.