Audras parents are both in their forties. the sum of their ages is ninety -two. the product of their ages is 2,107. how old is audras oldest parent?

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:

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

The new line segment CD is 1/4 th of AB

CD = × AB

Step-by-step explanation:

Given that, RSTU is a square and AB a line drawn through it's center.

let the length of side of square be a.

⇒ Length of line segment AB = a. (as it is same as length of side of square)

Now, given the square is dilated using the scale factor of 1/4 and a line is drawn through the center of the new dilated figure.

let this line be CD with points C and D on sides of dilated square.

Now, as the square is dilated by a factor of 1/4, length of side of dilated square is a× =

⇒ the length of CD =

⇒ The new line segment CD is 1/4 th of AB

CD = × AB