Question

a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages.

Answer 1

John is 9, Brian is 6.

Explanation:

I)

Let
`J` represent John's age and
`B` represent Brian's age.

John is three years older than Brian. In other words:

`J=B+3`

The product of their ages is 54. Or:

`JB=54`

II)

Write this as a quadratic by substituting:

`JB=54\\(B+3)B=54\\B^2+3B-54=0`

III)

Solve the quadratic:

`B^2+3B-54=0\\B^2-6B+9B-54=0\\B(B-6)+9(B-6)=0\\(B+9)(B-6)=0\\B=-9, 6`

Since age cannot be negative, Brian must be 6 years old right now.

John is three year older, so John is 9.