A pipe that is 136 inches long is cut into three parts whose lengths are in the ratio 3 : 5 : 9. Find the length of the shortest piece

Question

 A pipe that is 136 inches long is cut into three parts whose lengths are in the ratio 3 : 5 : 9. Find the length of the shortest piece

Answer 1

If the proportions are 3:5:9 for the three pieces, that means that you can think of this pipe as having 'x' subsections, each 17x in length [note that 3+5+9=17;  x is any positive value] that, when put together, make up the entire pipe.

 

Or, using proportions, a pipe of length 17 has subsections of 3:5:9 and the problem's pipe has subsections of 3x:5x:9x inches that, when put together, total 136 inches.

 

So, what is x for this problem ?     It is 136/17     and that is 8   [reminder: x does not have to be a whole number]

 

The length of the shortest piece is 3x  =  3*8   = 24 inches.

 

 

(note:  we do not have to find the length of the other subsections, until we want to check our answer)

 

Checking (very important, unless you are in a hurry on a timed test):

  The three pieces are 3*8, 5*8, and 9*8 inches long, does that total 136 inches  ?

                   3*8 + 5*8 + 9*8  = 136   ?

                     24 + 40 + 72  = 136    

                                136  = 136       yes!

Answer 2

3x + 5x + 9x = 136

17x = 136

x = 136/7

 

length of all the pieces are:

3 x 136/7, 5 x 136/7,  9 x 136/7

 

:)