Question

Administration 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 administration 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.) d^2 -13d<264
B.) 13d^2 <264
C.) d^2 -13 >264
D.) 13d^2 -d>264

Answer 1

A.) d^2 -13d < 264

Explanation:

The problem statement tells you d represents the number of desks in each row. It also tells you the number of rows is 13 fewer, so is (d-13). The number of desks in the rectangular array is the product of rows and desks per row, so is ...

total number of desks = d(d-13) = d^2 -13d

This value must be less than 264, so the inequality representing the limit on the number of desks is ...

d^2 -13d < 264 . . . . . matches selection A