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Solves Problems and Reasons Logically
Lesson 24
Construct Solutions
  Objectives/Vocab/Tips > Examples 1 | 2 | 3 | 4 > Practice: 1 | 2 | 3 | 4 > Reflection

Example 2:

Raymond and Boris went to the ball game last evening. They spent exactly $20.00 on hot dogs and soft drinks. They bought at least 5 hot dogs at $2.00 each and at least 5 soft drinks at $1.00 each.

  • What exactly did they buy?
  • What are two possible ways they bought the hot dogs and soft drinks?

Explain in detail how you found your answer using words, numbers, and/or pictures.

This problem would require an extended response which means you would be aiming to receive 4 points for your answer. In order to receive all 4 points be sure to thoroughly investigate the situation, use the given information to solve the problem, use applicable mathematical concepts and procedures, and finally construct a well stated, clear, valid solution using workable problem solving strategies.

To begin, make sure that you read over the problem again making sure you fully understand the problem. Remember, to help you, you can restate the problem in your own words as well. According to the problem, there must be at least two different outcomes of how Raymond and Boris bought hot dogs and soft drinks. With $20 spent, what did they buy?

Now let's look at a strategy or two that may be able to help us answer this problem. Let's make a table or a list and hopefully we will see a pattern as we begin with at least 5 hot dogs and 5 soft drinks.

At Least 5 Hot Dogs
+
At Least 5 Soft Drinks
=
$20
5(HD) x $2 = 10
+
10(SD) x $1 = $10
=
$20
6(HD) x $2 = $12
+
8(SD) x $1 = $8
=
$20
7(HD) x $2 = $14
+
6(SD) x $1 = $6
=
$20
8(HD) x $2 = $16
+
4(SD) x $1 = $4
=
$20

Using the information from the problem and know that there has to be at least 5 hot dogs and 5 soft drinks of each you can see that there are actually three possible outcomes to the problem. Notice that the last option, 8 hot dogs doesn't work as you could only buy 4 soft drinks and you needed to buy at least 5.

Now to answering the question and making sure you get the full 4 possible points. First, you would make sure that you include at least two possible outcomes as asked for by the question. It may even be to your advantage to list all three possible outcomes.

Next, be sure to show your table or list of using the facts given in the problem. SHOW how you solved the problem and came up with the different outcomes.

Be sure to include with your list or table a clear and specific explanation of how you went through the process of solving the problem. The more specific you are and don't leave anything out, will help you receive all 4 points.

Example 3 >>

 

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