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# The sum of Rose’s and Helen’s ages is 19, the sum of Rose’s and Amy’s ages is 22, the sum of Helen’s and Amy’s ages is 25. What is the age of the oldest girl?

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Given:

Sum of ages of Rose and Helen = 19

Sum of ages of Rose and amy = 22

Sum of ages of Helen and amy = 25

To Find :

The age of the oldest girl \begin{gathered}\\\end{gathered}

Solution :

Let ,

The age of Rose be x

The age of Helen be y

The age of Amy be z

We are given that Sum of ages of Rose and Helen as 19.

→ x + y = 19 (1)

Sum of ages of Rose and Amy is 22 (given)

→ x + z = 22 (2)

Now , Sum of ages of Helen and amy is 25 (given).

→ y + z = 25 (3)

Now adding eq(1) and eq(2) ,

→ x + y + x + z = 19 + 22

→ 2x + y + z = 41

Substituting the value of y + z from eq(3) ,

→ 2x + 25 = 41

→ 2x = 41 - 25

→ 2x = 16

→ x = 16/2

→ x = 8

Substituting the value of x in equation(1) we get ,

→ 8 + y = 19

→ y = 19 - 8

→ y = 11

Now , Substituting the value of y in eq(3) ;

→ 11 + z = 25

→ z = 25 - 11

→ z = 14

This mean ,

Age of Rose = x = 8 years

Age of Helen = y = 11 years

Age of Amy = z = 14 years

Amy is oldest girl among Helen and Rose.

Hence , The age of the oldest girl is 14 years.

Given:Sum of ages of Rose and Helen = 19Sum of ages of Rose and amy = 22Sum of ages of Helen and amy = 25To Find :The age of the oldest girl Solution :

Let ,

The age of Rose be xThe age of Helen be yThe age of Amy be z

We are given that Sum of ages of Rose and Helen as 19.

→ x + y = 19 ...........(1)

Sum of ages of Rose and Amy is 22 (given)

→ x + z = 22 ...........(2)

Now , Sum of ages of Helen and amy is 25 (given).

→ y + z = 25 ..........(3)

Now adding eq(1) and eq(2) ,

→ x + y + x + z = 19 + 22

→ 2x + y + z = 41

Substituting the value of y + z from eq(3) ,

→ 2x + 25 = 41

→ 2x = 41 - 25

→ 2x = 16

→ x = 16/2

→ x = 8

Substituting the value of x in equation(1) we get ,

→ 8 + y = 19

→ y = 19 - 8

→ y = 11

Now , Substituting the value of y in eq(3) ;

→ 11 + z = 25

→ z = 25 - 11

→ z = 14

This mean ,

Age of Rose = x = 8 yearsAge of Helen = y = 11 yearsAge of Amy = z = 14 years

Amy is oldest girl among Helen and Rose.

Hence , The age of the oldest girl is 14 years.

Rose - 8, Helen - 11, Amy - 14. Amy is oldest and her age is 14

Step-by-step explanation:

8 + 11 = 19

8 + 14 = 22

11 + 14 = 25

since 14 is the highest number, Amy is the oldest.

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