Elizabeth is 7 years older than Jared. The product of their ages is 60. How old is Elizabeth and Jared?

Answer 1

Given that:

The product of ages of Elizabeth and Jared is = 60

To Find:

Age of Jared = ?

Age of Elizabeth = ?

Solution:

Let the age of Jared be = x

Let the age of Elizabeth be = y

According to the given condition:

Product of ages of Elizabeth and Jared = xy =60 Years ------------------ (1)

Since Elizabeth is 7 years older than Jared, so:

y = x+7 ------------------------------ (2)

Putting the value of y in equation 1, we get;

x(x+7) = 60

x² + 7x = 60

OR x² + 7x - 60 = 0

By factorizing;

x² -5x +12x - 60 = 0

x(x-5) + 12(x-5) = 0

(x-5)(x+12) = 0

So, Either:

x-5 = 0 ; x+12 = 0

x = 5 ; x = -12

Since the age cannot be negative, so:

Age of Jared = x = 5 Years

From Equation 2;

Age of Elizabeth = y = x + 7 = 5 + 7

Age of Elizabeth = y =12 years