Question

Sarah is twice as old as Norah, If six years is subtracted from Norah's age and four years added
Sarah's age, then Sarah will be four times Norah's age. How old were they two years ago?

Answer 1

Answer:

The present age of Norah is 14 years old and Sarah is 28 years old.

Step-by-step explanation:

Given :

Sarah is = twice the age of Norah

When six years is subtracted from Norah's age and four years added Sarah's age, then Sarah will be four times Norah's age.

To find :

Their present age

Solution :

$\textsf{\underline{\underline{Let the present ages be -}}}$

• Norah as y
• Sarah as 2y

6 years subtracted from Norah's age = (y - 6)

4 years added to Sarah's age = (2y + 4)

$\rule{300}{1.5}$

$\textsf{\underline{\underline{According to the Question - }}}$

When six years is subtracted from Norah's age and four years added Sarah's age, then Sarah will be four times Norah's age.

$\bigstar \: \boxed{\sf{2y + 4 = 4(y - 6)}}$

$\sf{\implies} \: 2y + 4 = 4(y - 6) \\ \\ \sf{\implies} \: 2y + 4 = 4y - 24 \\ \\ \sf{\implies} \: 2y - 4y = - 24 - 4 \\ \\ \sf{\implies} \: - 2y = - 28 \\ \\ \sf{\implies} \: y = \dfrac{28}{2} \\ \\ \sf{\implies} \: y = 14$

Norah's present age = 14 years

$\rule{300}{1.5}$

★ Value of (2y)

$\sf{\implies} \: 2(14) \\ \\ \sf{\implies} \: 28$

Sarah's present age = 28 years

$\therefore$ The present age of Norah is 14 years old and Sarah is 28 years old.

Answer 2

Answer:

Suppose Norah age be y .

and Sarah age be 2y.

• ( y - 6 ) = ( six years subtracted from Norah's age ).
• ( 2y + 4 ) = ( four years added to Sarah's age ).

According to the Question:

if six years is subtracted from Norah's age and four years added in Sarah's age , then Sarah will be four times Norah's age .

Therefore: 2y + 4 = 4( y - 6 ) .

= 2y + 4 = 4( y - 6).

= 2y + 4 = 4y - 24.

= 2y - 4y = - 24 - 4.

- 2y = - 28.

y = 28

2

y = 14.

Therefore,Norah's present age = 14 years.

☆ Value of (2y) :

= 2 (14).

= 28.

Therefore ,Sarah's present age = 28 years .

Norah's present age = 14 years.

Sarah's present age = 28.