Geometry and Algebra word problem

Question

A line segent that is 23 ft to be divided into three pieces. The second piece is to be 4 ft less than twice the first piece, and the third piece is to be twice as long as the second piece. What will be the length of each piece?

 

Answer 1

Hi Henry,

 

This problem requires that we use 3 variables, so lets use X,Y, and Z to represent each of the sections on the line segment. This means that:

 

X+Y+Z=23.

 

Now we can interpret the second sentence using our 3 variables. The second piece(Y) is 4ft less than twice the first(X). Twice the first is then 2X and 4 feet less than this is 2X-4, which is equal to Y:

 

2x-4=y

 

Lastly, the third piece(z) is twice as long as the second piece(y):

 

z=2y.

 

Now we need to substitute these two expressions into the original equation (X+Y+Z=23) and because y is in both of the 2 other equations, the quickest way will be to substitute in expressions that contain Y. We will then need to solve the first for x and this gives us (y+4)/2=x

 

After we substitute in the 2 expressions containing y for x and z, we get: (y+4)/2+y+2y=23. 

 

Solve for y then plug this in to the other equations to get X and Z. 

 

y=6, z=12, x=5