The number of books checked out from the library varies directly with the number of book reports assigned. There were 3375 books checked out when there were 225 book reports assigned.
How many book reports have been assigned if there are 13,500 books
Since the number of books checked out varies directly with the number of book reports assigned we have the following relationship:
Let B be the number of books checked out and R be the number of reports due.
Then because R and B vary directly there is a constant K so that
B = K*R
If you prefer we could also use a different constant C and write
C*B = R.
For this particular problem,
3375 = K* 225
We can solve for K as
K= 3375/225 = 15.
So if the number of Reports R when there are 13500 books checked out is given by
13500=15*R
So R=13500/15=900. And this is our answer.
Another way to look at the problem is to recognize that for direct variation the ratio of the two quantities is a constant, so that we could set up the proportion:
225/3375 = R/13500
Cross multiplying gives
225*13500=3375*R
solving for R by dividing both sides by 3375 gives us
225*13500/3375 = 900 = R
To solve this problem, we need to determine the direct variation relationship between the number of books checked out and the number of book reports assigned.
Let's denote the number of books checked out as B and the number of book reports assigned as R. According to the problem, these variables are directly proportional, which means we can write an equation in the form B = kR, where k is the constant of variation.
To find the value of k, we can use the given information. We know that when there were 225 book reports assigned, 3375 books were checked out. We can substitute these values into the equation:
3375 = k * 225
To solve for k, divide both sides of the equation by 225:
k = 3375 / 225
k = 15
Now that we have the value of k, we can use it to find the number of book reports assigned when there are 13,500 books checked out. Let's denote this value as R2:
13,500 = 15 * R2
To solve for R2, divide both sides of the equation by 15:
R2 = 13,500 / 15
R2 = 900
Therefore, if there are 13,500 books checked out, there would be 900 book reports assigned.