Question 229587
Mary is 12 years older than her sister, Martha. The product of their ages is 540. How old is each?


Step 1.  Let x be the age of Martha.


Step 2.  Let x+12 be the age of Mary.


Step 3.  Then {{{x(x+12)=x^2+12x=540}}} since the product of their ages is 540.  


Step 4.  We can form a quadratic equation by subtracting 540 from both sides of the equation


{{{x^2+12x-540=cross(540)-cross(540)}}} 


{{{x^2+12x-540=0}}}


Step 4.  To solve, use the quadratic formula given as


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


where a=1, b=12 and c=-540.


*[invoke quadratic "x", 1, 12, -540]


Step 5.  Selecting the positive answer x=18 then x+12=30 and note the product of 18 and 30 is 540.


Step 6.  ANSWER:  Martha is 18 years old and Mary is 30 years old.


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J

S