Expert: Bobby Soltani - 8/2/2004

Question
I can solve equations when they are given to me in a math format but I don't know how to set up an equation or formula of my own from a word problem.  Please put the following problem in an equation form and solve.  Please explain how to do this. The problem is:

A foreman has 1200ft. of wire and needs enclose a plot so that the length will be 100ft. more than the width.  How long and wode will he make the plot?

Answer
Hi Rebecca,

These problems can be tricky to set up.  They get easier with practice.

We need to see what is given first.  We know that the total length (T) of the wire is 1200.  We also know that the length (l) is 100 ft more than the width (w).  In math terms, we can write these statements as
T = 1200
l = 100 + w

We also know that the the total wire (T) is equal to 2 times the length plus 2 times the width because if you imagine a rectangle, there are two sides of length and two sides of width.  This gives us another equation.
T = 2l + 2w or 1200 = 2l + 2w

So now we have two equations and two unknown variables.  These can be solved by substituting a variable from one equation into another like this
1) l = 100 + w
2) 1200 = 2l + 2w

let's plug l from equation one into equation 2.

1200 = 2*(100 + w) + 2w
1200 = 200 + 2w + 2w
1200 = 200 + 4w
1000 = 4w
w = 250

So now we know that the width is 250 and we can plug it in to the first equation to get the length.
l = 100 + w = 100 + 250 = 350

So the length would be 350 ft.

I hope this explanation helps.  Let me know if you have any other questions.

Bobby