The age of Sari is 8 years.
The age of Justin is 9 years.
Explanation:
Let x denote the age of Justin.
Let y denote the age of Sari.
Given that the product of their age is 72.
Thus, it can be written in equation as
![xy=72](https://tex.z-dn.net/?f=xy%3D72)
Since, the numbers x and y are consecutive integers and Justin is older, then, it can be written as,
![x=y+1](https://tex.z-dn.net/?f=x%3Dy%2B1)
Therefore, the two equations are
and ![x=y+1](https://tex.z-dn.net/?f=x%3Dy%2B1)
<u>The ages of Sari and Justin:</u>
The ages of Sari and Justin can be determined by solving the two equations.
Let us solve the equations using substitution method.
Substituting
in the equation
, we have;
![(y+1)y=72](https://tex.z-dn.net/?f=%28y%2B1%29y%3D72)
![y^2+y=72](https://tex.z-dn.net/?f=y%5E2%2By%3D72)
![y^2+y-72=0](https://tex.z-dn.net/?f=y%5E2%2By-72%3D0)
Factoring the equation, we get;
![(y-8)(y+9)=0](https://tex.z-dn.net/?f=%28y-8%29%28y%2B9%29%3D0)
![y=8 \ or \ y=-9](https://tex.z-dn.net/?f=y%3D8%20%5C%20or%20%5C%20y%3D-9)
The value of y cannot be negative.
Thus,
is the value of y.
Substituting
in the equation
, we have;
![x=8+1](https://tex.z-dn.net/?f=x%3D8%2B1)
![x=9](https://tex.z-dn.net/?f=x%3D9)
Thus, the value of x is 9.
Therefore, the age of Sari is 8 years and the age of Justin is 9 years.