SOLUTION: One sister is older than the other by 5 years. The product of their ages is twice the age of their mother who is 33. What is the age of the older sister? Setup the equation so

One sister is older than the other by 5 years.
The product of their ages is twice the age of 
their mother who is 33. What is the age of 
the older sister? 
Setup the equation
solve the equation
write the answer

Let the younger sister's age be x


>>...One sister is older than the other by 
     5 years...<<

Translation:  The older siste's age is x + 5

>>...The product of their ages is twice the 
     age of their mother who is 33...<<

Erase the unnecessary words "the age of their 
mother who is". So it now reads

>>...The product of their ages is twice...33...<<

Replace "twice...33"" by 66

>>...The product of their ages is 66<< 

Replace the words "the product of their ages" by 
     "x(x + 5)". So now it reads:

>>...x(x + 5) is 66...<<

Replace the word "is" by " = ".  That gives 
us our equation:

              x(x + 5) = 66

Remove the parentheses:

               x² + 5x = 66

Get 0 on the right side

          x² + 5x - 66 = 0

Factor the left side:

       (x + 11)(x - 6) = 0

Set each factor = 0

     x + 11 = 0 gives x = -11
      x - 6 = 0 gives x = 6

Discard the negative answer.

So the younger sister's age is x = 6 
    years.

The older sister's age is x + 5 
    which is 6 + 5 = 11 years.

Edwin