One number is eight times another number. Determine the two numbers of the sum of their reciprocals is 9/16

Answer 1

X = 8Y

1/X + 1/Y = 9/16

16Y + 16X = 9XY <--- multiplies both sides by 16xy

16y + 16(8y) = 9(8y)y <--- substitutes x = 8y

16y + 128y = 72y^2

144y = 72y^2

2y = y^2

0 = y^2 - 2y

0 = y(y-2)

y=0 does not have a reciprocal, so it disqualified

y-2=0 ---> y = 2

2 and 16

CHECK

1/2 + 1/16 = 8/16 + 1/16 = 9/16

Yes, 2 and 16