A 50ft rope is cut into two pieces. The length of one piece is 9 times the length of the other. What is the length of the longer piece?

x + y = 50 eq1

x = 9y eq2

plug in eq2 to eq1 to solve for y..

9y + y = 50

10y = 50

 y = 5

now plug in the value of y to eq1, to solve for x..

x = 9(5) = 45 ft

Therefore, the length of the longer piece is 45 ft..

A 50ft rope is cut into two pieces. 

The length of one piece is 9 times the length of the other. 

The length of the longer piece is 45 feet.

Say that the shortest is 1, then the other piece must be 1*9 = 9.

Thus the total = 1 + 9 = 10. that's not 50; it doest work.

say the shortest is 2. Then the other piece must be 2*9 = 18.

Thus the total is [left for you]? making a total of [?]. Does it work?

Say the shortest is 3. Then the other is ...[?]. etc.

Continue the process till you get the answer [or near it].

Show your work here and your answer. Once you would have done that, I will show you another way how to solve this.

Hopefully no one will spoil you the answer. That would be very irresponsible of them. And don't forget to vote me best answer for being the first to correctly walk you through and for not giving you the explicit answer. That way it gives you a chance to work at it and to get good at it.

x + 9x= 50; x= 5

9*5= 45 ft