9.6: Fruit Confusion
Look at the picture of the bananas and the information about the price of bananas below. Can you figure out how much just one banana would cost? In this concept, we will use proportions and logical reasoning to determine the cost of individual items given information about multiples of those items.
Guidance
In order to answer a question about the cost of an item like the one above, we can use the problem solving steps to help.
- First, describe what you know. What do we know about the weight of the fruit? What do we know about the cost of the fruit?
- Second, identify what your job is. In these problems, your job will be to figure out the cost or weight of one piece/pound of fruit. Or, it might be to figure out how many pieces of fruit are in a closed box.
- Third, make a plan . In these problems, your plan should be to write a proportion that relates the weight of the fruit to the cost. Solve the proportion and use logical reasoning to answer the question that was asked.
- Fourth, solve . Implement your plan.
- Fifth, check . Check your answer by verifying that it works with all of the original information.
Example A
Look at the pictures below and answer the question.
Solution:
We can use problem solving steps to help us.
Example B
Look at the pictures below and answer the question.
Solution:
We can use problem solving steps to help us.
Example C
Look at the pictures below and answer the question.
Solution:
We can use problem solving steps to help us.
Concept Problem Revisited
We can use problem solving steps to help us.
Vocabulary
A proportion is an equation that states that two ratios are equal. In this concept, we can use proportions because the ratio of weight to cost is constant for each type of fruit. As long as we know the cost of fruit for a particular weight of that fruit, we can find the cost of that fruit for any weight of that fruit using proportions.
Guided Practice
1.
2.
3.
Answers:
1. , so , and .
2. , so is , and is 10.
3. , so , and
Practice
Image Attributions
Description
Learning Objectives
Students use proportions and logical reasoning to answer questions about the cost and weight of fruit. Students use problem solving steps to help.