A car salts business will lease a property and has 5080 doll

A car salt\'s business will lease a property and has 5080 dollars (a month) budgeted for this. The property will be a fenced square lot. Such lots lease for 2 dollars a square foot (per month), and the fencing rents for 0.4 dollars a linear foot (per month). What size lot can the business afford with this budget?

Solution

Let the dimensions of the leased property that the car sales business can rent be x ft by x ft. Then the area of the plot is x² sq ft and the length of the fencing is 4x ft.The rent for this property is 2x²+0.4*4x =2x²+1.6 x so that 2x² + 1.6 x = 5080. On multiplying both the sides by 2.5, we get 5x² + 4x –12700 = 0. Now, on using the quadratic formula, we get x = [-4±{(4)²–4*5*(-12700)}]/2*5 =[-4±( 16 + 254000)]/10 = (-4±254016)/10 = (-4+± 504)/10. Since x cannot be negative, we have x = (-4+504)/10 = 500/10 = 50 ft.Thus, the car sales business can lease a fenced square lot of 50 ft by 50 ft = 2500 sq. ft.

Note: the solution to the equation ax² +bx +c = 0, as per the quadratic formula is x = [ -b ± (b² -4ac)]/2a