The square of Mark's age 3 years ago is 6 times the age he will be in 9 years. What is his age now?

1 Answer
Mar 16, 2018

15 years old

Explanation:

If we denote Mark's age today by #x# we can set up an equation to solve.

We know that #(x-3)^2#, "the square of his age three years ago", is 6 times greater than "his age in 9 years", #(x+9)#, so to make this problem solvable we must create an expression where these two equal each other.

Thus by multiplying #(x+9)# by 6, we set "his age in 9" years to be equal to "the square of his age 3 years ago", creating the following expression:

#(x-3)^2=6(x+9)#

Which, when simplified, leads us to a quadratic equation:

#x^2-12x-45=0#

#0=(x-15)(x+3)#

Hence the two possible answers are:

#x_1=15# and #x_2=-3#

Obviously, you cannot be -3 years old, so he must be 15 years old.