Mark is draining his pool to clean it. at 12: 00 p. m., he started to drain the pool. at 4: 00 p. m., the pool had 11,600 gallons of water. at 7: 00 p. m., the pool had 6,800 gallons of water. if draining the pool is modeled by a linear function, how many gallons of water were initially in the pool? a) 15,600 b) 18,000 c) 19,400 d)21,200

12:00 P.M. to 7:00 P.M. is a total of 7 hours.
4:00 P.M. to 7:00 P.M. is a total of 3 hours.

This means that from 4:00 p.m to 7:00 P.M. this represents 3/7 of what was lost from 12:00 P.M. to 7:00 P.M.

After knowing this, after doing 11,600 - 6,800 = 4,800
4,800 represents 3/7 of what was lost for 7 hours.
We then divide 4,800 by 3 which gets 1,600.

Because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.  After adding 11,200 to how much water was left at 7:00 P.M. which was 6,800. 11,200 + 6,800 = 18,000

This means that the pool originally had 18,000 gallons in the pool.

You can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.