Question

Dean needs 6060 inches of wood to build a rectangular picture frame.
The length, l,l, of the frame is twice its width, ww.

Three of these equations give the correct value for ww.
Which equation does NOT?


2⋅(2w+w)=602·2w+w=60

w+2w+w+2w=60w+2w+w+2w=60

2⋅w+2⋅2w=602·w+2·2w=60

w+2w=60

Answer 1

What we know:
Perimeter=60
Perimeter formula=2l+2w
l=2w

This perimeter has the following set up using p=60 and l=2w:
perimeter =2(l)+2w
60=2(2w)+2w 
60=4w+2w
60=6w

Now that we know how many w's we need to have we can use this information to find which equations have 6 w's and which one does not.
Look at the first equation:
2(2w+w)=60         distributive power
4w+2w=60               like terms
6w=60                       correct

second equation:
w+2w+w+2w=60
6w=60              like terms, correct

third equation:
2w+2x2w=60            multiplication property
2w+4w=60                  like terms
6w=60                          correct

fourth equation:
w+2w=60                     like terms
3w=60                              not correct

Fourth equation is not correct.