Pregunta
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width of the veranda if its area is to be ,
10 A father’s age is the square of his son’s age , In 20 years’ time the father will be three times
as old as his son. What are the ages of the father and son?

Ask by Fitzgerald Joseph. in Australia
Mar 15,2025

Solución de inteligencia artificial de Upstudy

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The son is 8 years old, and the father is 64 years old.

Solución

Let’s break down the problem into two parts: the veranda’s width and the ages of the father and son.

Part 1: Width of the Veranda

We know that the area of the veranda is given as . However, we need more information about the shape of the veranda (e.g., length) to find the width. If we assume the veranda is rectangular, we can express the area as:
Let be the length and be the width. Thus, we have:
Without additional information about the length, we cannot determine the width. If you have a specific length in mind, please provide it.

Part 2: Ages of the Father and Son

Let be the son’s current age. According to the problem:
  1. The father’s age is the square of his son’s age:
  2. In 20 years, the father will be three times as old as his son:
Now, we can substitute the expression for from the first equation into the second equation:
Now, let’s simplify and solve for :
Rearranging gives us:
Now, we will solve this quadratic equation using the quadratic formula:
where . Let’s calculate the discriminant and the roots.
Calculating the discriminant:
Now, substituting into the quadratic formula:
Calculating the two possible values for :
  1. (not a valid age)
Thus, the son’s age is . Now, we can find the father’s age:

Summary of Results

  • The son’s age is years.
  • The father’s age is years.
If you provide the length of the veranda, I can help you find the width as well.

Respondido por UpStudy AI y revisado por un tutor profesional

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Bonus Knowledge

To find the dimensions of the veranda, you can start from the area formula for rectangles: . If we assume the length to be a fixed value and the area is , you can easily find the corresponding width by rearranging the formula. For example, if the length is , the width would be . Play around with various lengths to see how the width changes!
Now, moving on to the ages: Let’s denote the son’s age as . According to the problem, the father’s age is . In 20 years, the son’s age will be and the father’s age will be . The equation becomes . Simplifying that leads to a quadratic equation. Solving it will give you both the father’s and son’s current ages!

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