Question

Administrators at a local high school are organizing desks in the cafeteria for the junior students to use while taking a practice SAT test. Due to space limitations, there should be fewer than 264 students in the cafeteria. The administrators want there to be 13 less rows than the number of desks in each row. If d represents the number of desks in each row, which inequality could represent this situation?

A: 13d^2 < 264
B: 13d^2 -d > 264
C: d^2 -13d < 264
D: d^2 - 13 > 264

Answer 1

Answer: The correct option is C, i.e.,
`d^2-13d<264`.

Explanation:

It is given that the total number of students in cafeteria should be less than 264. The administrators want there to be 13 less rows than the number of desks in each row.

Let the number of desks in each row be d.

Since administrators want there to be 13 less rows than the number of desks in each row. So the number of row is d-13.

In one row the number of desks is d. So in (13-d) rows the number of number of desks is d(d-13).

Since the total number of students in cafeteria should be less than 264. So we get,

`d(d-13)<264`

`d^2-13d<264`

Therefore, the correct option is C.