The sum of two consecutive integers is 59. Write an equation that models this situation and find the values of the two integers.

The two consecutive integers are 29 and 30

Work Shown:

x = first integer

x+1 = second integer that follows immediately after x

Consecutive integers are numbers like {4,5,6,7,...} ones that follow right after another.

Add up those expressions and set the sum equal to 59. Then solve for x

x+(x+1) = 59

2x+1 = 59

2x = 59-1

2x = 58

x = 58/2

x = 29

So 29 is the first number

x+1 = 29+1 = 30

and 30 is the next number

As a check, 29+30 = 59 which confirms our answer.

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.

step-by-step explanation: