SOLUTION: A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $2.50 per foot and the cost of preparing the soil is $0.60 per ft2, determine the size

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $2.50 per foot and the cost of preparing the soil is $0.60 per ft2, determine the size       Log On


   

Question 571033: A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $2.50 per foot and the cost of preparing the soil is $0.60 per ft2, determine the size of the garden that can be enclosed for $257.60.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = length in feet of a side of the garden
given:
cost of fence is +2.5%2A4%2As+=++10s+ dollars
------------
The area of the garden is +s%5E2+
Cost of preparing soil is +.6%2As%5E2+
+.6s%5E2+%2B+10s+=+257.6+
.6s%5E2+%2B+10s+-+257.6+=+0+
+6s%5E2+%2B+100s+-+2576+=+0+
+3s%5E2+%2B+50s+-+1288+=+0+
Use quadratic formula

+b+=+50+
+c+=+-1285+
+s+=+%28+-50+%2B-+sqrt%28+50%5E2+-+4%2A3%2A%28-1288%29+%29%29+%2F+%282%2A3%29+
+s+=+%28+-50+%2B-+sqrt%28+2500+%2B+15456+%29%29+%2F+6+
+s+=+%28+-50+%2B-+sqrt%28+17956+%29%29+%2F+6+
+s+=+%28+-50+%2B+134%29+%2F+6+ ( ignore the (-) square root )
+s+=+84%2F6+
+s+=+14+
The size of the garden is 14 x 14 ft2
check answer:
+.6s%5E2+%2B+10s+=+257.6+
+.6%2A14%5E2+%2B+10%2A14+=+257.6+
+.6%2A196+%2B+140+=+257.6+
+117.6+%2B+140+=+257.6+
+257.6+=+257.6+
OK