Question 280026
Not wanting to be embarrassed by revealing her age on her birthday, Grandma instead told the grandkids that if they multiplied her age in 5 years by 5, then multiplied her age in 6 years by 6, and added the two totals together, they would get a number that is 12 times her current age.  When she saw the large wax forest fire atop her birthday cake , Grandma knew they had figured it out. How old is she? 

let her age be x now

after 5 years

(x+5)*5

after 6 years

(x+6)*6


5(x+5) +6(x+6) = 12x

5x+25+6x+36=12x

11x+61=12x

12x-11x=61

x=61