Dorothy is 10 years older then her brother. If the product of their ages is 231, how old is dorothy?

D * b = 231

d = b + 10

b (b + 10) = 231

b^2 + 10b = 231

b^2 + 10b - 231 = 0

(b - 11) (b + 21) = 0

b - 11 = 0

b = 11 < = = brothers age

b + 21 = 0

b = - 21 ... extraneous solution ... does not work

d = b + 10

d = 11 + 10

d = 21 < = = dorothy's age

so dorothy is 21 and her brother is 11

Hi, Dorothy is 21 years old and her brother is 11 years old, because 21 times 11 equals to 231, the product of their ages is 231, in other words when you multiply those two ages you will get 231.