If (64) x =(48) y =(36) z then show that 1/x +1/z = 2/y

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1 Answer

64x = 48y = 36z

Three equations:

64x = 48y

48y = 36z

1/x + 1/z = 2/y

The third equation is true if solving this system of equations results in an "always true" statement like 2 = 2 or 37 = 37.

64x = 48y

48y = 36z

1/x + 1/z = 2/y

divide the first equation by 64 on both sides and the second equation by 36 on both sides

x = (48/64)y

(48/36)y = z

1/x + 1/z = 2/y

simplify

x = (3/4)y = 3y/4

z = (4/3)y = 4y/3

1/x + 1/z = 2/y

plug the x and z values from the first and second equation into the third equation:

1/(3y/4) + 1/(4y/3) = 2/y

solve

4/(3y) + 3/(4y) = 2/y

multiply both sides by 12y

16 + 9 = 24

25 = 24

This is never true, so if (64) x =(48) y =(36) z then 1/x +1/z does not equal 2/y.

answered Aug 21, 2014 by johnperkins Level 13 User (103k points)

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