Positive integers x and y have a product of 56 and

x is less than y

Seven times the reciprocal of the smaller number plus 14 times the reciprocal of the larger integer equals 4. what is the value of x?

sinclairdragon428 Jun 10, 2019

#2**+1 **

x * y = 56..............................(1)

7*1/x + 14*1/y = 4...................(2)

Can you solve the 2 simultaneous equations? Try it.

Guest Jun 10, 2019

edited by
Guest
Jun 10, 2019

#3**+1 **

xy = 56 ⇒ y = 56/x

And

7 (1/x) + 14(1/y) = 4

7/x + 14/y = 4

7/x + 14 / (56/x) = 4

7/x + (14/56)x = 4

7/x + (1/4) x = 4 multiply through by 4x

28 + x^2 = 16x rearrange as

x^2 - 16x + 28 = 0 factor as

(x - 14) ( x - 2) = 0

Set each factor to 0 and solve for x and we have that

x = 14 or x = 2

And y =

56/14 = 4 or 56/2 = 28

So (x,y) = (2, 28)

CPhill Jun 10, 2019