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
c = checked out
r = reports
c = kr
3375 = k*225
k = 15
----------------------
13500 = 15r
r = 900
The area of a classroom space per student varies inversely with the number of students in the room. When there are 15 students in the room, each student has 20 sq ft of space.
How many square feet of space are available per student when there are 25 students in the classroom?
A. 60 sq ft
B. 33 sq ft
C. 12 sq ft
D. 20 sq ft
To solve this problem, we need to use the concept of direct variation. Direct variation is a relationship between two variables where one variable is a constant multiple of the other variable. In other words, as one variable increases or decreases, the other variable also increases or decreases by the same factor.
In this case, the number of books checked out from the library (books) varies directly with the number of book reports assigned (reports). We can represent this relationship as:
books = k * reports
where k represents the constant of variation.
To find the value of k, we can use the given information that when there were 225 book reports assigned, 3375 books were checked out from the library.
Plugging these values in the equation, we have:
3375 = k * 225
To solve for k, we divide both sides of the equation by 225:
k = 3375 / 225
k = 15
Now we have the value of k, which is 15.
To find the number of book reports assigned if there are 13,500 books checked out, we can use the equation:
books = k * reports
Substituting the values we have:
13,500 = 15 * reports
Dividing both sides of the equation by 15:
reports = 13,500 / 15
reports = 900
Therefore, if there are 13,500 books checked out from the library, 900 book reports have been assigned.