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?

Question

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?

UpStudy AI · Accepted Answer

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 $$ 24 \, \mathrm{m}^2 $$. 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:

$$
\text{Area} = \text{Length} \times \text{Width}
$$

Let $$ L $$ be the length and $$ W $$ be the width. Thus, we have:

$$
L \times W = 24
$$

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 $$ x $$ be the son's current age. According to the problem:

1. The father's age is the square of his son's age:
   $$
   F = x^2
   $$

2. In 20 years, the father will be three times as old as his son:
   $$
   F + 20 = 3(x + 20)
   $$

Now, we can substitute the expression for $$ F $$ from the first equation into the second equation:

$$
x^2 + 20 = 3(x + 20)
$$

Now, let's simplify and solve for $$ x $$:

$$
x^2 + 20 = 3x + 60
$$

Rearranging gives us:

$$
x^2 - 3x + 20 - 60 = 0
$$

$$
x^2 - 3x - 40 = 0
$$

Now, we will solve this quadratic equation using the quadratic formula:

$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$

where $$ a = 1, b = -3, c = -40 $$. Let's calculate the discriminant and the roots.

Calculating the discriminant:

$$
D = b^2 - 4ac = (-3)^2 - 4(1)(-40) = 9 + 160 = 169
$$

Now, substituting into the quadratic formula:

$$
x = \frac{-(-3) \pm \sqrt{169}}{2(1)} = \frac{3 \pm 13}{2}
$$

Calculating the two possible values for $$ x $$:

1. $$ x = \frac{16}{2} = 8 $$
2. $$ x = \frac{-10}{2} = -5 $$ (not a valid age)

Thus, the son's age is $$ x = 8 $$. Now, we can find the father's age:

$$
F = x^2 = 8^2 = 64
$$

### Summary of Results

- The son's age is $$ 8 $$ years.
- The father's age is $$ 64 $$ years.

If you provide the length of the veranda, I can help you find the width as well.
The son is 8 years old, and the father is 64 years old.

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?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Part 1: Width of the Veranda

Part 2: Ages of the Father and Son

Summary of Results

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions

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?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Part 1: Width of the Veranda

Part 2: Ages of the Father and Son

Summary of Results

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions

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?