Respuesta :
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
[tex]xy=72[/tex]
Since, the numbers x and y are consecutive integers and Justin is older, then, it can be written as,
[tex]x=y+1[/tex]
Therefore, the two equations are [tex]xy=72[/tex] and [tex]x=y+1[/tex]
The ages of Sari and Justin:
The ages of Sari and Justin can be determined by solving the two equations.
Let us solve the equations using substitution method.
Substituting [tex]x=y+1[/tex] in the equation [tex]xy=72[/tex], we have;
[tex](y+1)y=72[/tex]
[tex]y^2+y=72[/tex]
[tex]y^2+y-72=0[/tex]
Factoring the equation, we get;
[tex](y-8)(y+9)=0[/tex]
[tex]y=8 \ or \ y=-9[/tex]
The value of y cannot be negative.
Thus, [tex]y=8[/tex] is the value of y.
Substituting [tex]y=8[/tex] in the equation [tex]x=y+1[/tex], we have;
[tex]x=8+1[/tex]
[tex]x=9[/tex]
Thus, the value of x is 9.
Therefore, the age of Sari is 8 years and the age of Justin is 9 years.
