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.