Proportional Relationships in Tables Quick Check
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Question
Use the table to answer the question.
Time (hours) Pages read
12 15
1 30
112 45
2 60
Ruth can read 15 pages in 30 minutes. She decides to create a table to keep track of her progress. From the data provided, at what ratio is the constant of proportionality?
(1 point)
Responses
(15, 12)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis
(112, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis
(2, 60)
left parenthesis 2 comma 60 right parenthesis
(1, 30)
left parenthesis 1 comma 30 right parenthesis
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The correct answer is:
(1, 30)
left parenthesis 1 comma 30 right parenthesis
To find the constant of proportionality, you need to determine the ratio between the pages read and the corresponding time in hours.
First, identify two sets of values that have a proportional relationship. In this case, you can choose the values (12, 15) or (1, 30) because they both represent a time and the pages read.
For the first option: (12, 15), the ratio would be 15/12. To simplify this ratio, you can divide both numbers by their greatest common factor, which in this case is 3. Dividing 15 by 3 gives you 5 and dividing 12 by 3 gives you 4. So, the simplified ratio is 5/4.
For the second option: (1, 30), the ratio would be 30/1. Simplifying this ratio by dividing both numbers by their greatest common factor, 30/1 simplifies to 30/1.
Out of the given choices, the correct ratio for the constant of proportionality is:
(1, 30)
To determine the ratio of the constant of proportionality, we need to find the ratio between the number of pages read and the corresponding time in hours.
Looking at the table, we can see that Ruth reads 15 pages in 30 minutes, which is equivalent to 0.5 hours.
So, the ratio of the constant of proportionality is:
15 pages : 0.5 hours
Simplifying this ratio, we get:
30 pages : 1 hour
From the given response options, the correct answer is:
(15, 12)