...number? whose product is 24, and the difference of their cuba : cube of their difference : : 19 : 1. What are the numbers. Let x= the greater number, and y= the lesser. Then, xy=24,and x3— y3 : (x—y)3 : : 19 : 1. By expansion, x3-y'J : x3—3x:ly+3xy3—y...

...numbers whose product is 24, and the difference of their cubes : cube of their difference : : 19:1. What are the numbers ? Let x= the greater number, and y= the lesser. Then, zy=24, and x2— y2 : (x—y)2 : : 19 : 1. By expansion, x2 — y2 : x2 — 3x2y + 3xy2...

...twice the less, when added, are twentytwo, and twice the greater is six more than three times the less. What are the numbers ? Let x = the greater number, and y = the less number. (1.) By one condition of the question, 3 x -j-2 y = 22. (2.) By another condition ...........

...is to the greater as 7 to 5 ; and it' the sum be multiplied by the greater, the product will be 126. What are the numbers ? Let x = the greater number, and y the lesS. By the question, x + y : x : : 7 : 5, (1) and xy + y' = 126. (2) The value of x derived from...

...numbers exceeds the equirational mean by 13, and the equirational exceeds the harmonic mean by 12 ; what are the numbers ? Let x = the greater number, and y = the less ; then, by the question, 13 ...... (a), and L + 12 = v*y ...... (6). Multiplying the corresponding...

...and the result divided by the greater of the two numbers, the quotient is 2 and the remainder 2. Find the numbers. Let x = the greater number, and y = the smaller number. Then ^=-5 = 4, y and x + From the solution of these equations x = 47, and y = 11. Let x = number of...

...and the result divided by the greater of the two numbers, the quotient is 2 and the remainder 2. Find the numbers. Let x = the greater number, and y — the smaller number. Then ÍÜZ-? _ 4, and From the solution of these equations, x = 47 and y = 11. Let x = number of dollars...

...long would it last them both ? CASE IV. 1. The sum of two numbers is a, and their difference is b ; what are the numbers ? Let x = the greater number, and y = the smaller numher. Then, x+y = a, and x—y==b. a + b Whence x = and y = 2 a—b 2 These formulas, expressed in...

...times the greater number is divided by twice the smaller, the quotient is 11 and the remainder 4. Find the numbers. Let • x = the greater number, and y = the smaller number. Then, ï = 7 + i (1) У У 3£=ll + ± (2) 2y 2y From(l), x=7y + 4 (3) From (2), 3x=22y + 4 (4) 3X(3)is...

...8520 ; В, ?440. 2. Half the sum of two numbers is 20, and three times their difference is 18. Find the numbers. Let x = the greater number, and y = the smaller number. Then ^.У = 20 (!) ft and 3 (x - y) = 18 (2) Multiply (1) by 2, and divide (2) by 3. x + y - 40 (3)...