find three consecutive odd integers such that the sum of the first, two times the second and three times the third is 82.

choose the mathematical translation for the given situation.

a.

6 x plus 16 equals 82

6x+16=82

b.

6 x plus 8 equals 82

6x+8=82

c.

3 x plus 3 equals 82

3x+3=82

d.

3 x plus 6 equals 82

3x+6=82

A

Step-by-step explanation:

Let the first odd integer = x

Let the second odd integer = (x+2)

This is because adding 2 to x makes it an odd integer. If 1 is added, it would become an even integer.

Let the third odd integer = (x+2)+2

= (x+4)

The sum of the first, two times the second and three times the third is written as

x + 2(x+2) + 3(x+4) = 82 (open the bracket)

x + 2x+ 4+ 3x + 12 = 82 (collect like terms)

x + 2x + 3x + 4 +12 = 82

6x + 16 =82 (this is the mathematical translation)

6x = 82 - 16

6x = 66

Divide both sides by 6

6x/6 = 66/6

x = 11

The first odd integer= 11

The second odd integer = x + 2

= 11 + 2

= 13

The third odd integer = x + 4

= 11+4

= 15

The consequtive odd integers are 11, 13 and 15

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.