Answer:
d. 66 years
Step-by-step explanation:
Let:
Man's age in 2013 = x
Son's age in 2013 = y
Then:
Man's age in 2010 = x-3
Son's age in 2010 = y-3
Man's age in 2011 = x-2
Son's age in 2011 = y-2
"The age of a man is 9 times as old as his son in 2010." can be written as:
(x-3) = 9(y-3)
x - 3 = 9y - 27
x = 9y - 24 ... [1]
"In 2011, his age is equal to the square of his son's age." can be written as:
(x-2) = (y-2)²
x = (y-2)² + 2
x = y² - 4y + 6 ... [2]
We substitute [1] into [2], then we have:
9y - 24 = y² - 4y + 6
y² - 13y + 30 = 0
(y-3)(y-10) = 0
y = 3 or 10
** y is impossible equals to 3 because in 2010, the son's age is y-3, that means the son's age will be 0 if y = 3, which is inapplicable. Therefore y = 10 years old.
[1]
x = 9y - 24
= 9(10) - 24
= 66 years
