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Sarah is 4 times as old as her niece now. in 8 years, she will be twice as old as her niece then. how old is each now?

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by marmaduke

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by marmaduke

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Present: Niece's age = x

Sarah's age = 4x

In 8 years (+8) : Niece's age = x + 8

Sarah's age = 2 (x+8)

Equation:

4x = 2 (x+8)

Solution:

4x = 2 (x+8)

4x = 2x + 16

4x - 2x = 16

2x = 16

__2__x = __16__

2 2

x = 8

Substitute 8 for x:

Present Ages: Niece's age = x

= 8 years old

Sarah's age = 4x

= 4 (8)

= 24 years old

FINAL ANSWER: Present age: Niece is 8 years old and Sarah is 24 years old

TO Check their ages in 8 years:

Niece's age = x + 8

= 8 + 8

= 16 years old in 8 years (future)

Sarah's age is twice her niece's age in 8 years (future)

= 2 (x + 8)

= 2 (8 + 8)

= 2 (16)

= 32 years old

Sarah's age = 4x

In 8 years (+8) : Niece's age = x + 8

Sarah's age = 2 (x+8)

Equation:

4x = 2 (x+8)

Solution:

4x = 2 (x+8)

4x = 2x + 16

4x - 2x = 16

2x = 16

2 2

x = 8

Substitute 8 for x:

Present Ages: Niece's age = x

= 8 years old

Sarah's age = 4x

= 4 (8)

= 24 years old

FINAL ANSWER: Present age: Niece is 8 years old and Sarah is 24 years old

TO Check their ages in 8 years:

Niece's age = x + 8

= 8 + 8

= 16 years old in 8 years (future)

Sarah's age is twice her niece's age in 8 years (future)

= 2 (x + 8)

= 2 (8 + 8)

= 2 (16)

= 32 years old