Question

One number is 6 times another. The sum of their reciprocal id 14/3. Find the numbers.

Answer 1

Let
x-------> one number
y--------> another number

we know that
x=6y--------> equation 1
(1/x)+(1/y)=14/3-----> (x+y)/xy=14/3-----> 3*(x+y)=14xy-----> equation 2

I substitute 1 in 2
3*(6y+y)=14(6y)y------> 21y=84y²-----> y=0.25
x=6y-----> x=6*0.25-----> x=1.5

the answer is
the numbers are 1.5 and 0.25