Two step equations

Question

187 in. long pipe is cut into three pieces such that the second piece is thirteen in. more than the first piece, and the third piece is twenty in. more than eight times the second piece.

Answer 1

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!

Answer 2

Let L = length of the first piece

L + 13 = 2nd piece

8(L + 13) = 3rd piece

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

10L + 137 = 187

10L = 50

L = 5

L + 13 = 18

8(L + 13) + 20 = 144

 

You should now take the answers and make sure they satisfy the original problem.