Divide 10 into two parts in such a way that when a certain one of these...

 

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Divide 10 into two parts in such a way that when a certain one of these parts is divided by the other and the fraction is multiplied by its numerator, the result gives 9. Problem 54. Find a number such that if 7 is added to it and the sum multiplied by the root of 3 times the number, then the result is 10 times the number. [Hint: To 1 solve the equation (x+7)3x=10x, put x=y, this yields y+21=10y.] 3 Problem 66. Divide 10 into two parts in such a way that when 50 is divided by one part and 40 by the other, and then the fractions are multiplied, 125 will result. [Hint: Algebraically, the equations are x+y= 10 and 50 40 x y = 125.] Divide 10 into two parts in such a way that when a certain one of these parts is divided by the other and the fraction is multiplied by its numerator, the result gives 9. Problem 54. Find a number such that if 7 is added to it and the sum multiplied by the root of 3 times the number, then the result is 10 times the number. [Hint: To 1 solve the equation (x+7)3x=10x, put x=y, this yields y+21=10y.] 3 Problem 66. Divide 10 into two parts in such a way that when 50 is divided by one part and 40 by the other, and then the fractions are multiplied, 125 will result. [Hint: Algebraically, the equations are x+y= 10 and 50 40 x y = 125.]