The cost of leveling a 1560yd2 rectangular at the rate of .50 per square yard. Also find the cost to fence it

Question

The cost of leveling a 1560yd2 rectangular at the rate of .50 per square yard. Also find the cost to fence it if it code 2.50 per yard. And the width of the playground is 32 yd

Answer 1

Word (story) problems are easy to solve if you can “picture” it – so, draw a rectangle and label the width (W=32) and a length (L=?) and an area (A = L*W = 1560 yd²).

Already, we find the length (by putting W into the formula for A,

         L * 32 – 1560

         L = 1560 / 32

         L = 48.75    (or 48 feet 9 inches)

Now, remember that the fence is the Perimeter = L + W + L + W  =  2*L + 2*W

           P = 2*1560 + 2*48.75

The cost of the fence is $2.50/yd and there are 3217.5 yds  (and the yds cancel, leaving $):

          Cost of fence = 2.50 *3217.5

             Cost of fence = $8043.75   (part of answer)

Now, the Cost of leveling = 1560 yd² * $0.50/yd²     (and the yd² cancels out, leaving $):

          Cost of leveling = $780     (part of answer)

And, checking our answers often reveals errors, so let’s do that:

    Is  1560 * 0.50 = 780  ?     Yes

   Is  3217.5 * 2.50 = 8043.75  ?    Yes

Finally, if asked, you may report L as either 48.75 feet   or as 48 feet 9 inches  (which is preferred?)