Tracy and Vanessa are buying rocks for each
of their fish tanks. The pet store uses different
tags and a chart to show the prices of the rocks.
For example, if a rock is in the basket with a
triangle tab, then the price is 3 rocks for $1.00.
Also, if a tag has a star on it, then the rocks
in the basket are on sale for half-price.
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Basket Tags
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Price of Rocks
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Basket Tags
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Price of Rocks
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3 for $1.00
|
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2 for $1.50
|
|
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2 for $1.00
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3 for $2.00
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Tracy bought 3 rocks from the basket with a hexagon
and star and 6 rocks from the basket with a square.
Vanessa bought 4 rocks from the basket with a
circle and 3 rocks from the basket with a triangle.
Who spent more money on rocks?
- Tracy
- Vanessa
- They spent the same amount.
Show how you got your answer using words, numbers,
or pictures. |
Let's begin solving this problem
by using the six step problem solving process.
Step 1: Make
sure that you understand the problem. An excellent way to to be sure you understand the
problem is to restate the problem in your own words,
as if you were explaining the problem to someone
else.
In this problem there are two girls buying rocks
for their fish tanks. Using the given chart and information
about the cost of the different rocks, you need to
find which girl spent more money on the rocks.
Step 2: To analyze
the data given in the problem,
you want to organize the facts and numbers you are
given in this problem.
- Tracy bought 3 rocks with the hexagon and a
star and 6 rocks with a square.
- Vanessa bought 4 rocks with the circle and 3
rocks with a triangle.
Step 3: To solve
this problem you could make a simple
chart or table to show how much each girl spent on
the rocks. Using the different operations within
the table you will arrive at the correct answer.
Step 4: Make
an estimate or a guess as to who you
think might have spent the most on rocks by looking
at the data and not figuring the problem out.
Since Tracy has rocks that have a star on it, this
means that the rocks are on sale, meaning she could
have spent less since they are half price. Our estimate,
Vanessa paid more for the rocks.
Step 5: Solve
the problem using a table to see the
answer.
|
Rocks
|
Tracy
|
Price Adjustment
|
| 3 rocks |
hexagon and star |
$2 for 3 rocks, star makes half
price, so $1 for 3 rocks |
| 6 rocks |
square |
$1 for 2 rocks, 3 sets of rocks, $3 |
| |
TOTAL |
$4 |
Rocks |
Vanessa |
Price
Adjustment |
| 4 rocks |
circle |
$1.50 for 2, 2 sets so, $3 |
| 3 rocks |
triangle |
$1.00 for 3, 1 set so, $1 |
| |
TOTAL |
$4 |
Step 6: Looking at our solutions, you
find that both girls spent the same amount on rocks for their
fish tanks. As you look at your choices you find
that choice C gives you the option you are looking
for. Therefore the first part or answer to the problem
is C, both girls spent the same amount of money on
the rocks.
To finish this problem, an explanation of your
solution is required. Remember, be specific, be clear, and
be complete in your explanation.
Your explanation can include the tables you made
to solve the problem, but be sure to include an explanation
of what you did in making your tables and why. You
can even include your 6 steps used to solve the problem.
To receive the two points for this problem, make
sure that you answer the question for 1 point and
then for the other point have a complete explanation.
Your explanation may look like this:
In this problem I had to find who spent the
most money on rocks for their fish tank. To find
out what Tracy spent on the rocks I know she
bought 3 rocks with the hexagon tag, meaning
the cost of those three rocks was $2, but since
they also have a star on the tag, they are half
price. Therefore, I know that those three rocks
really cost $1. She also bought 6 rocks with
a square tag. That means that for every 2 of
those rocks it cost $1. Since she bought 3 sets
of those to make 6 total, she spent $3 on those
rocks for a total of $1 + $3 for a total of $4.
Vanessa
bought 4 rocks with a circle tag which is
2 for $1.50. So 4 of these rocks would be
two times $1.50 for a total of $3. Next she
bought 3 rocks with
the triangle tag which are 3 for $1. Add the two sets of rocks together and
you get $3 + $1 which is also $4, just like
Tracy.
This
shows that both girls spent the same amount
of money on the rocks, $4. |
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