Ex. 2. A person, selling a horse for $72, finds that his loss per
cent is one-eighth of the number of dollars that he paid for the horse :
what was the cost price ?
Suppose that the cost price of the horse is x dollars ; then the loss on $100 is ${x}{8}.
Hence the loss on $x is x x {x}{800}, or {x^2}{800} dollars ; the selling price is x — {x^2}{800} dollars.
Hence x — {x^2}{800} = 72, or x^2 - 800x + 57600 = 0; that is, (x - 80) (x - 720) =0 ; x = 80, or 720 ;
and each of these values will be found to satisfy the conditions of the problem. Thus the cost is either $80, or $720.
Ex. 3. A cistern can be filled by two pipes in 33{1}{3} minutes ; if the larger pipe takes 15 minutes less than the smaller to fill the cistern, find in what time it will be filled by each pipe singly.
Suppose that the two pipes running singly would fill the cistern in x and x — 15 minutes. When running together they will fill ({1}{x} + {1}{x - 15}) of the cistern in one minute. But they fill {1}{33{1}{3}} , or {3}{100} of the cistern in one minute ; hence {1}{x } + {1}{ x-15 } = {3}{100}, 100(2x-15) = 3x(x-15), 3x^2-245x +1500 = 0, (x-75)(3x-20)=0; x = 75, or 6{2}{3}.
Thus the smaller pipe takes 75 minutes, the larger 60 minutes. The other solution, 6{2}{3} , is inadmissible.
Ex. 4. The small wheel of a bicycle makes 135 revolutions more than the large wheel in a distance of 260 yards ; if the circumference of each were one foot more, the small wheel would make 27 revolutions more than the large wheel in a distance of 70 yards: find the circumference of each wheel.
