Answer: Hello there!
Let's define x = age of parent 1, and y = age of parent 2, and suppose that y is the oldest one.
we know that:
x + y = 92
x*y = 2107
now we have a system of equations that we need to solve:
the first step is isolate one of the variables in one of the equation, let's isolate x in the first equation:
x = 92 - y
now we can replace it in the second equation and find the value of y.
x*y = 2107
y*(92 - y) = 2107
92y - y^2 = 2107
now we need to solve a cuadratic equation!
-y^2 + 92y - 2107 = 0
using the Bhaskara formula, we get:
[tex]y = \frac{-92 +/- \sqrt{92^{2} -4 *(-1)*(-2107) } }{-2} = \frac{-92 +/- \sqrt{36} }{-2} = \frac{-92 +/- 6}{-2}[/tex]
so we have two solutions:
y = (-92 + 6)/(-3) = 43
y = (-92 - 6)/(-2) = 49
because y is the oldest one, we need to take the biggest solution, this is y = 49.
so the oldest parent has 49 years.
if you want to find the age of the other parent, replace this in the first equation:
y + x = 92
49 + x = 92
x = 92 - 49 = 43
