Question 229118
S = smaller number
L = larger number


S = 2L/3 (equation 1)


1/S + 1/L = 1/6 (equation 2)


Multiply both sides of equation 2 by S*L.


1/S + 1/L = 1/6 becomes:


L + S = (S*L)/6


Multiply both sides of this equation by 6 to get:


6L + 6S = S*L


Replace S with (2L)/3 to get:


6L + 6*(2L)/3 = L*2L/3


Remove Parentheses to get:


6L + 12L/3 = 2L^2/3


Multiply both sides of equation by 3 to get:


18L + 12L = 2L^2


Combine like terms to get:


30L = 2L^2


Divide both sides of equation by 2 to get:


15L = L^2


Subttract 15L from both sides of equation to get:


L^2 - 15L = 0


Factor L to get:


L*(L-15) = 0


Solve for L to get:


L = 0
or:
L = 15


Substitute these in original equations to get:


S = 2L/3 becomes:


S = 2*0/3 = 0
or:
S = 2*15/3 = 10


When S = 0 and L = 0, then 1/S + 1/L = 1/6 becomes:


1/0 + 1/0 = 1/6 which is false so L = 0 is not a valid answer and can be rejected.


When S = 10 and L = 15, then 1/10 + 1/15 = 1/6.


Multiply both sides of of this equation by 30 to get:


3 + 2 = 5 which is true so L = 15 is good.


Your answer is L = 15 and S = 10.


The larger number is 15 and the smaller number is 10.