Page 255. (3.) Let a denote one number, and y the other. Then, by the conditions, Substituting for 2, in Equation (2), we have, 16y+ y2+ y2 = 34; Let a denote the first number, and y the second. Substituting the value of y2, from Equation (1), we have, (5.) Let x denote the less, and y the greater. Then, by the conditions, and 34y2 41650; = y2 = = 1225; or, y = 35. Hence, the numbers are 21 and 35. (6.) Let denote the less number, and y the greater. Then, by the conditions, y x = 7; whence, y = x + 7, x(x+7) 2 + 30 = x2; or, x2 + 7x + 60 = 2x2; (8%) Let the numbers be denoted by x and y. Combining (1) and (3), we find, x= 2, and y = 3. (8.) Let x denote the greater, and y the less. Then, by the conditions, Substituting these values of x and x2, in Equation (2), we Let a denote the distance, in miles, traveled by A, and y, the distance traveled by B. Now, the rate of travel, or the distance traveled in a single day, will be found by dividing the distance by the number of days; hence, Now, the entire distance traveled by A, divided by what he traveled in 1 day, will give the time he was traveling; and the same for B. But these times are equal; hence, Substituting the value of 22, from Equation (1), we have, which, after performing the operations indicated, gives, y = 54, and, consequently, x = 72, (11.) Denote the less number by x. Then the greater will be denoted by x + 15; and we shall have, |