My brother is three years older than I am. The product of our ages is 54, How old am I?

Question

Need some help

Really hard

Answer 1

If your age is x, then your brother's age is (x+3)

Multiplying the two ages gives a product of 54:

 

x(x+3) = 54

x² + 3x = 54

x² + 3x - 54 = 0

This can be factored.  The factors of -54 that add to 3 are 9(-6).

(x+9)(x-6) = 0

x = -9   or  x = 6

 

Since your age will not be a negative number, you are 6 years old.

Your brother is (x+3) = 9 years old.

Answer 2

n = your age

 

n + 3 = your brother's age

 

n(n + 3) = 54

 

n² + 3n - 54 = 0

 

(n + 9)(n - 6) = 0

 

n = -9 or 6, but it cannot be negative, so n = 6

 

You are 6 years old, your brother is 6+3 = 9 years old.