Question

A girl is twice as her sister. Five years hence the product of their ages is 375. Find their present ages.​

Answer 1

Answer:

Sister's age is 10 years

Girls'age is 20 years

Step-by-step explanation:

Let the sister's age be x

Then the girl's age will be 2x

After 5 years the sister's age will be x+5

And girl's age will be 2x+5

According to the question the product of their ages will be 375

Therefore the equation will be

(x+5) (2x+5) = 375

2x²+5x+10x+25 = 375

2x²+15x = 350

2x²+15x-350=0

As we have got a quadratic equation, we will factorise it.

We will split the middle term in such a way that the product of the coefficients of the numbers will be equal to the coefficients of the first and second term

Which will be 2x²-20x+35x+350=0

Factorising, 2x(x-10)+35(x-10)=0

(2x+35) (x-10) = 0

This is possible if one the terms is equal

So, 2x+35 = 0 or x-10=0

x= -35/2 or x = 10

As the age cannot be negative we will take the value of x as 10

So the sister's age is 10 years and the girl's age is 2×10=20 years

HOPE IT HELPS

PLEASE MARK AS BRAINLIEST

Answer 2

Step-by-step explanation:

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Given :-

Boy is Twice as old as his Brother.

Five years hence the product of their ages is 375.

Solution :-

Lets Assume That, His brother Present age is = x years.

Than, Boy Present age = 2 * x = 2x years.

A/q,

→ After 5 years His brother will be = (x + 5) years old.

→ Boy will be = (2x + 5) years old.

So,

→ (x + 5) * (2x + 5) = 375

→ 2x² + 5x + 10x + 25 = 375

→ 2x² + 15x + 25 - 375 = 0

→ 2x² + 15x - 350 = 0

Splitting The Middle Term now,

→ 2x² - 20x + 35x - 350 = 0

→ 2x(x - 10) + 35(x - 10) = 0

→ (x - 10)(2x + 35) = 0

Putting both Equal to Zero now,

→ x - 10 = 0

→ x = 10

Or,

→ 2x + 35 = 0

→ 2x = (-35)

→ x = (-35/2) ≠ Negative Value of age Not Possible.

Hence,

→ His Brother Present Age = x years = 10 years.

→ And, Boy Present Age = 2x years = 2*10 = 20 years.

So,

Boy is 20 years old now, and His brother is 10 years old now.