Question

divide 27 into two parts such that the sum of their reciprocals is 3/20

Answer 1

Answer:

15 & 12

Step-by-step explanation:

Let x and y be 2 parts

forming equations through given data =>

x + y = 27    (A) or x = 27 - y

1/x + 1/y = 3/20    (B)

substituting from A, value of x

=>  1/(27-y)  + 1/y = 3/20

=>  (y + 27 - y)/(27y - y²) = 3/20

=>  180 = 27y - y²

=> y² - 27y + 180 = 0

(y -15)(y-12) = 0

y = 15,12

Hence x = 12,15 respectively

Therefore, 2 parts are 15 & 12

Answer 2

Let number = x

Another number = 27 - x

According to question;

1/x + 1/(27 - x) = 3/20

(27 - x + x)/(27x - x²) = 3/20

Cross-multiply,

20(27) = 3(27x - x²)

540 = 81M - 3x²

x² - 27x + 180 = 0

x² - 15x - 12x + 180 = 0

x(x - 15) -12(x - 15) = 0

(x - 12) (x - 15) = 0

x = 12, 15