Word problem

Question

A rectangular lot whose perimeter is 290 feet is fenced along three sides. An expensive fencing along the lots length costs $20 per foot and an enexpensive fencing along the two side widths costs only $7 per foot. The total cost of the fencing along the three sides come to $2540. What are the lots dimensions. 

Answer 1

A careful reading of the problem reveals:

  A perimeter of 290 feet = L + W + L + W

 

The cost of fencing along the length (L) is $20/foot.  At L feet, that cost is (L ft)($20/ft) = $20L

The inexpensive along the two sides (2W) is $7/ft.  At 2W feet, that cost is (2W ft)($7/ft) = $14W

The fencing for the three sides costs:   $20L + $14W = $2540

 

O.K., the math (let's use the elimination method):

     20L + 20W = 2900     (first equation rewritten; times 10)

     20L + 14W = 2540     (second equation)

  ------------------------    (elimination:  subtract equations)

               6W  =  360

                 W = 60             (divide both sides by 6)

 

Again, use elimination:

    2L + 2W = 290     (first equation)

            2W = 120     (previous answer times 2)

  --------------------   (elimination:  subtract equations)

    2L          = 170

          L = 85

 

Checking (very important):

  Is 2(60) + 2(85) = 290    ?

      120 + 170  = 290    ?

         290 = 290    ?yes

 

  Is  (20)(85) + (7)(120) = 2540    ?

       1700 + 840 = 2540    ?

         2540 = 2540    ?yes

Answer 2

290 = 2(l + w)

145 = l + w

145 - l = w

 

20l + 7w + 7w = 2540      combine like terms

20l + 14w = 2540             substitute for w

20l + 14(145 - l) = 2540   distribute

20l + 2030 - 14l = 2540    combine like terms

6l + 2030 = 2540              subtract 2030 from both sides

6l = 510                            divide both sides by 6

l = 85

 

The length of the lot is 85 feet and the width is 60 feet.

 

Check

 

20(85) + 2(7)(60)

1700 + 840

2540