Question

the ages of sari and justin can be represented as two consecutive integers. The product of their age is 72. Justin is older. write and solve an equation to find their ages

Answer 1

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

$xy=72$

Since, the numbers x and y are consecutive integers and Justin is older, then, it can be written as,

$x=y+1$

Therefore, the two equations are $xy=72$ and $x=y+1$

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 $x=y+1$ in the equation $xy=72$, we have;

    $(y+1)y=72$

       $y^2+y=72$

$y^2+y-72=0$

Factoring the equation, we get;

$(y-8)(y+9)=0$

$y=8 \ or \ y=-9$

The value of y cannot be negative.

Thus, $y=8$ is the value of y.

Substituting $y=8$ in the equation $x=y+1$, we have;

$x=8+1$

$x=9$

Thus, the value of x is 9.

Therefore, the age of Sari is 8 years and the age of Justin is 9 years.