One number is 5 times another. The sum of their reciprocals is 2/5. Determine the smaller number.

So x=5y

reciprocal of x=1/x then

sum of reciprocals means 1/x+1/y=2/5

subsitute x=5y for x in 1/x+1/y=2/5 and get

1/5y+1/y=2/5

multiply 1/y by 5/5 to make it 5/5y so you can add since the denomenators (bottom number) are the same

1/5y+5/5y=2/5

6/5y=2/5

multiply both sides by 5y

6=2y

divide both sides by 2

3=y

put this into x=5y so

x=5 (3)

x=15

y=3