Question

James is four years younger than Austin. If 2 times James age is increased by the square of austins age, the result is 28. Find the 2 ages. Use an algebraic solution

Answer 1

Let the age of Austin be a, then the age of James is a-4.

"If 2 times James age is increased by the square of Austins age, the result is 28."

means: $2(a-4)+ a^{2} =28$

rearrange the quadratic equation and solve it:

$a^{2}+2(a-4)-28=0$

$a^{2}+2a-8-28=0$

$a^{2}+2a-36=0$

add and subtract 1 to complete the square:

$a^{2}+2a+1-1-36=0$

$(a+1)^{2} =37$

a+1=root 37 = 6 (approximately), so a=5 

or a+1=root 37 = -6 (approximately), so a=-7, which is not possible

The age of Austin is 5, and the age of James is 1.