Question

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?

Answer 1

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.