A 28-inch rope is to be cut into two pieces so that one piece is 9 inches longer than twice the other. How long is each piece, if a = 2, b = 9, and l = 28?

Question

whpalmer4 · Answer

Let a and b be the respective lengths of rope.

a + b = 28
a = 2*b + 9

Combine the two:

28 = a + b = (2*b + 9) + b = 3*b + 9
Subtract 9 from both sides and divide both sides by 3:
19/3 = b

So the short piece is 6 1/3 inches long.  The longer piece is twice that plus 9, or 21 2/3 inches long.  Add them together and they add to 28, so the answer checks out.

anonymous · Answer

thank you very much for the explanation