Question

At the first pep rally of the season, the football team and the volleyball team were presented to the student body. During the pep rally, up to 11 players talked to the crowd. Football players talked about 17 seconds each and volleyball players talked about 28 seconds each.

If the players only had a total of 242 seconds (4.03 minutes), which system of inequalities could be used to determine the number of football players (f) and volleyball player! (v) that could talk to the student body?

A. f+ y< 11 17f+ 287< 242
B. ftv< 11 17y + 28% < 242
C. f+ v< 11 176+ 28v< 242
D. ftv< 11 17v+28f< 242​

Answer 1

A. f + y ≤ 11

17f + 287 ≤ 242

Explanation:

[] Let f be football players and v be volleyball players.

-> The total time must be less than or equal to 242 seconds.

-> If football players talked for 17 seconds, we can write it as 17f.

-> If volleyball players talked for 28 seconds, we can write it as 28v.

[] Coming back to the first point I made, the total time must be less than or equal to 242 seconds.

-> 17f + 28v ≤ 242

[] This is going to be a part of our system of inequalities

-> Because of this, we rule out the following options.

B & D - the football players talk for 17 seconds, not the volleyball players

C ​ - not less than or equal too, only less than

[] This leaves us with the option of A.

-> The first part of it also works. If 11 players can talk to the crowd, then the total of f and v must be equal too or less than 11.

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather