A 12-foot board is divided into two pieces so one piece is twice as long as the other. What are the lengths?

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Answer 1 · 2017-08-28T10:02:13

Shorter piece: #4# #"ft."#

Longer piece: #8# #"ft."#

The two pieces are such that one piece is twice as long as the other.

So if the length of the shorter piece is #x#, the length of the other must be #2 x#.

Then, the total length is #x + 2 x = 12# #"ft." Rightarrow 3 x = 12# #"ft."#.

If we solve the equation #3 x = 12# #"ft."# for #x#, we will find the length of the shorter piece:

#Rightarrow 3 x = 12# #"ft."#

#therefore x = 4# #"ft."#

So the length of the longer piece is #2 x = 2 times 4# #"ft."# #= 8# #"ft."#.