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?
A. (1, 30)
B. (1 1/2, 30)
C. (2, 60)
D. (15, 1/2)
To find the constant of proportionality, we need to determine the ratio of pages to minutes. Ruth can read 15 pages in 30 minutes, so the ratio is 15:30. To simplify the ratio, we can divide both numbers by 15:
15 ÷ 15 = 1
30 ÷ 15 = 2
So the ratio of pages to minutes is 1:2.
Therefore, the constant of proportionality is C. (2, 60).
To determine the ratio of the constant of proportionality, we need to find the relationship between the number of pages read and the time taken to read those pages.
We know that Ruth can read 15 pages in 30 minutes. This can be expressed as a ratio:
15 pages : 30 minutes
To simplify the ratio, we can divide both sides by the greatest common divisor, which is 15:
15 pages ÷ 15 : 30 minutes ÷ 15
This simplifies to:
1 page : 2 minutes
Therefore, the ratio of the constant of proportionality is:
A. (1, 30)
To find the ratio of the constant of proportionality, we need to identify a relationship between the number of pages Ruth can read and the amount of time it takes her.
Given that Ruth can read 15 pages in 30 minutes, we can set up a proportion using the ratio of pages read to time taken.
Let's use the variable "x" to represent the constant of proportionality.
The proportion can be set up as:
15 pages / 30 minutes = x pages / 1 minute
To solve for "x," we cross-multiply:
15 minutes * x pages = 30 minutes * 1 page
15x = 30
Now let's solve for "x" by dividing both sides of the equation by 15:
x = 30 / 15
x = 2
Therefore, the ratio of the constant of proportionality is 2 pages per minute.
Looking at the answer options:
A. (1, 30): This doesn't match the ratio we found.
B. (1 1/2, 30): This doesn't match the ratio we found.
C. (2, 60): This matches the ratio we found, where the constant of proportionality is 2 pages per minute.
D. (15, 1/2): This doesn't match the ratio we found.
Thus, the correct answer is C. (2, 60).