David has a hose that is 27 ft long. He wants to cut it into two pieces so that the longer piece is 3 ft more than 2 times the length of the shorter piece.

How long will each piece of hose be?

Shorter piece:
ft
Longer piece:
ft

Question

David has a hose that is 27 ft long. He wants to cut it into two pieces so that the longer piece is 3 ft more than 2 times the length of the shorter piece.
 
How long will each piece of hose be?
 
Shorter piece:   
 ft
Longer piece:    
 ft

anonymous · Answer

Hi there! We need to write a couple of equations so that we can solve this.
Let's call the two pieces x and y

x + y =27
x = 2y + 3

do you see where i got these equations from?

senia01 · Answer

yes x+y+27 is the shorter piece+longer piece= the hose

anonymous · Answer

Cool. So now we have to solve these.

x = 27 - y

substitute this into x = 2y + 3

(27-y)=2y+3

anonymous · Answer

And solve that equation to find y

senia01 · Answer

8?

anonymous · Answer

Perfect. Now that you have y, you can find x.

x + y = 27
Substitute y = 8 and solve for x

anonymous · Answer

Let x be the length of the shorter piece of rope.
Solve the following for x:
x + (2 x + 3) = 27

senia01 · Answer

so the longer piece is 19 and the shorter piece is 8?

anonymous · Answer

Yes.

senia01 · Answer

Can you help me with one more?

anonymous · Answer

I'l try.