The reciprocal of a number is added to three. The result is the quotient of 25 and the number. Find the number

  8

Step-by-step explanation:

Let x represent the number. Then the reciprocal is 1/x. The quotient of 25 and the number is 25/x. The problem statement tells us ...

  3 + 1/x = 25/x

Subtracting 1/x, we have ...

  3 = 24/x

  x = 24/3 = 8 . . . . . . . . multiply by x/3

The number is 8.

step-by-step explanation:

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.