Question

James is four years younger than Austin. If three times James age is increased by the square of Austin's age, the result is 28. Find the ages of James and Austin.

Answer 1

James = 1 year

Austin = 5 years

Explanation:

Let James age = x

Let Austin's age = y

James is four years younger than Austin.

x = y - 4

If three times James age is increased by the square of Austin's age, the result is 28.

3(x - 4) + y² = 28

Hence,

Note: x = y - 4

Hence,

3y - 12 + y² = 28

3y + y² - 12 - 28 = 0

y² + 3y - 40 = 0

y² + 8y - 5y - 40 = 0

y(y + 8) - 5(y + 8 ) = 0

(y + 8)(y - 5)

y = -8

y = 5 years

x = y - 4

x = 5 - 4

x = 1 years.