How do i divide a 6 and 3/4 inch line into three parts so that each part is 1/4 inch shorter than the others before it

  2 1/2, 2 1/4, 2

Step-by-step explanation:

Let x represent the first part. Then the next part is (x -1/4), one-quarter inch shorter. The part after that is ((x -1/4) -1/4), one-quarter inch shorter still.

The sum of these three parts is 6 3/4:

  x + (x -1/4) + (x -1/2) = 6 3/4

  3x -3/4 = 6 3/4 . . . . . . . . . . . . collect terms

  x -1/4 = 2 1/4 . . . . . . . . . . . . . . divide by 3

  x = 2 1/2 . . . . . . . . . . . . . . . . . add 1/4

So, the first piece is 2 1/2; the next piece is 1/4 shorter, so is 2 1/4; and the last piece is 1/4 shorter still, so is 2 inches.

The pieces are 2 1/2 inches, 2 1/4 inches, and 2 inches long.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.