Question

James and billy have ages that are two consecutive odd integers whose products is 399. Use a quadratic equation to find out the age of each boy if james is the younger of the two boys?

I dont understand how to make the equation and please provide the answers

Answer 1

Ages of James and billy are `19 and 21` years respectively.

Explanation:

Let the two consecutive odd integers be `(2 n-1) and (2 n+1)`

Their product is `(2 n-1)(2 n+1)=399` or

`(2 n)^2- 1^2= 399 or 4 n^2= 399+1 or 4 n^2=400`

`:. n^2= 400/4 or n^2= 100 :. n = +- 10 :. n = 10`

Since age cannot be negative `n!=-10`.

When `n=10 , 2 n-1= 19 and 2 n +1= 21` Therefore,

ages of James and billy are `19 and 21` years respectively. [Ans]