Ishwar S. answered • 07/06/18

University Professor - General and Organic Chemistry

Hello Adam

Your question does not state what exactly you want to solve, but I will assume that you want to solve for the length of each piece of pipe.

Allow p to equal the length of the first piece.

"the second piece is thirteen in. more than the first piece." For this, we can write the relationship as 13 + p

"the third piece is twenty in. more than eight times the second piece." For this, we can write the relationship as 20 + 8(13 + p)

The sum of the length of all 3 pieces must equal 187 in. We can combine the above relationships and write the equation as:

1st piece + 2nd piece + 3rd piece = 187

p + (13 + p) + (20 + 8(13 + p)) = 187

p + 13 + p + 20 + 104 + 8p = 187

10 p + 137 = 187

Subtract 137 from both sides

10 p + 137 - 137 = 187 - 137

10 p = 50

p = 5

Length of the 1st piece =

**5 in.**Length of 2nd piece = 13 + p = 13 + 5 =

**18 in.**Length of 3rd piece = 20 + 8(13 + p) = 20 + 8(13 + 5) = 20 + 8(18) = 20 + 144 =

**164 in.****To verify, sum of the lengths of all 3 pieces must equal 187 in.

5 + 18 + 164 = 187!