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

Algebra.Com
Question 74625: 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
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

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:

               x˛ + 5x = 66

Get 0 on the right side

          x˛ + 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
RELATED QUESTIONS

Eliasbeth is 6 years older than her sister elisa. Their mother's age is twice the sum of... (answered by sudhanshu_kmr)
Sally has two older siblings. Her brother is 2 years older than she is. Her sister is... (answered by josgarithmetic)
Jason is 6 years older than his sister. Their mother is years older than the sum of their (answered by mxgirl22)
Dolor had a sister who is 2 years older than twice her age the sum of their ages is 23... (answered by ankor@dixie-net.com)
There are three little girls. The youngest is two years old and the eldest is eight years (answered by ikleyn)
Erin has an older sister and a younger sister. Her older sister is one year more than... (answered by ewatrrr)
Dawn’s mother is 4 years older than twice Dawn’s age. The difference of their ages is 22 (answered by josgarithmetic)
John is five years older than his sister. The product of their present ages is 150. (answered by ikleyn)
Dawn's mother is 4 years older than twice dawn's age. The difference of their age is 22... (answered by macston)