a million. permit the form of 5c funds be x. hence, the form of 10c funds is 3x, and the form of 25c funds is (3x + 2). the completed value of the 5c funds is 0.05x, the completed value of 10c funds is 0.3x and the completed value of 25c funds is (0.25)(3x + 2) = 0.75x + 0.5 as a result the completed value of all funds is = 0.05x + 0.3x + 0.75x + 0.5 = a million.1x + 0.5 all of us comprehend that a million.1x + 0.5 = 4.ninety, so we ve: a million.1x = 4.4 x = 4 as a result there are 4 5c funds, twelve 10c funds and fourteen 25c funds. 2) permit the quantity invested in the corporate be x and the quantity put in the mark downs financial business enterprise be y. x + y = 2500 y= 2500 - x --- (a million) (0.06)x + (0.05)y = 141 --- (2) utilising (a million) and (2), we ve: (0.06)x + (0.05)(2500 - x) = 141 0.06x + one hundred twenty five - 0.05x = 141 6x + 12500 - 5x = 14100 x = 1600 because x = 1600, y = 2500 - 1600 = 900 as a result, he invested $1600 in the corporate and $900 in the financial business enterprise. 3) After a million.5 hr, the bus travelled: (a million.5)(50) = seventy 5 miles The bus is travelling at 50mph, while the motor vehicle is travelling at 75mph. hence, each and every hour, the motor vehicle won seventy 5 - 50 = 25 miles over the bus. Distance between bus and vehicle on the beginning up = seventy 5 miles. Time mandatory to overhaul bus = seventy 5 / 25 = 3 hr Time stunning now = 4am + a million.5 hr = 5.30am Time whilst vehicle overtake bus = 5.30am + 3hr = 8.30am 4) permit the form of rooms rented on the beginning up be x. permit the unique value of room be y. hence, we ve: 28800 = xy y = 28800 / x --- (a million) The form of rooms rented now could be (x + 6). the value now could be (y - 20). the completed quantity earned proceed to be unchanged, so we ve: 28800 = (x + 6)(y - 20) --- (2) Substituting (a million) into (2), we can get: 28800 = (x + 6)((28800 / x) - 20) 28800x = (x + 6)(28800 - 20x) 28800x = -20x^2 + 28680x + 172800 20x^2 + 120x - 172800 = 0 x^2 + 6x - 8640 = 0 (x - ninety)(x + ninety six) = 0 x = ninety or x =-ninety six (Rejected, because value won t be ready to be unfavourable). as a result, ninety rooms have been rented out on the beginning up on the unique value. 5) permit the unique velocity be x. New velocity = (x + 5) hence, we ve: (20 / x) + (20 / (x + 5)) = a million 20(x + 5) + 20x = x(x + 5) 20x + a hundred + 20x = x^2 + 5x x^2 - 35x - a hundred = 0 utilising the quadratic formulation, we ve: x = [35 +/- sqrt((-35)^2 + 4(a hundred))] / 2 x = (35/2) +/- (a million/2)sqrt(1625) the value won t be ready to be unfavourable, so the unique velocity would desire to be (35/2) + (a million/2)sqrt(1625) km/hr