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Jimmy reads 15 pages in 5 minutes. Carlo reads 12 pages in 6 minutes. Find each constant of proportionality, showing your work. Then write a sentence to compare the proportional relationships.(2 points)
To find the constant of proportionality, we need to divide the number of pages by the number of minutes for each person.
For Jimmy:
Constant of proportionality = 15 pages / 5 minutes = 3 pages/minute
For Carlo:
Constant of proportionality = 12 pages / 6 minutes = 2 pages/minute
To compare the proportional relationships, we can say that for every minute, Jimmy reads 3 pages while Carlo reads 2 pages.
To find the constant of proportionality for Jimmy's reading rate, we can divide the number of pages he reads (15) by the time it takes him (5 minutes).
Constant of proportionality for Jimmy: 15 pages / 5 minutes = 3 pages/minute
To find the constant of proportionality for Carlo's reading rate, we can divide the number of pages he reads (12) by the time it takes him (6 minutes).
Constant of proportionality for Carlo: 12 pages / 6 minutes = 2 pages/minute
Comparing the two proportional relationships, we see that Jimmy reads 3 pages per minute while Carlo reads 2 pages per minute. Therefore, Jimmy reads at a faster rate than Carlo.
To find the constant of proportionality for each person, we can use the formula k = y / x, where k is the constant of proportionality, y is the dependent variable, and x is the independent variable.
For Jimmy:
Jimmy reads 15 pages in 5 minutes.
So, the constant of proportionality for Jimmy is k = 15 / 5 = 3.
For Carlo:
Carlo reads 12 pages in 6 minutes.
So, the constant of proportionality for Carlo is k = 12 / 6 = 2.
To compare the proportional relationships, we can make a sentence like this:
"For every 1 minute, Jimmy reads 3 pages, whereas Carlo reads 2 pages."
This sentence illustrates that Jimmy's reading rate is faster than Carlo's, as Jimmy reads 3 pages in 1 minute, while Carlo only reads 2 pages in 1 minute.