# Algebra

Rosa is 14 years older than her sister amy. Three years ago, she was three times as old as amy. how old is each girl now?

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1. ages now:
Amy --- x
Rosa --- x+14

Three years ago:
Amy --- x-3
rosa ---- x+11

x+11 = 3(x-3)
x+11 = 3x - 9
2x = 20
x = 10

sub into my definitions

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2. R = Age of Rosa

A = Age of Amy

Rosa is 14 years older than her sister Amy.

R = A + 14

Three years ago, she was three times as old as amy

Three years ago, Rosa and Amy was 3 years younger so.

R - 3 = 3 ( A - 3 )

Replace R with A + 14

A + 14 - 3 = 3 ( A - 3 )

A + 11 = 3 A - 3 * 3

A + 11 = 3 A - 9 Add 9 to both sides

A + 11 + 9 = 3 A - 9 + 9

A + 20 = 3 A Subtract A to both sides

A + 20 - A = 3 A - A

20 = 2 A Divide both sides by 2

20 / 2 = 2 A / 2

10 = A

A = 10

R = A + 14

R = 10 + 14

R = 24

Rosa is 24 year old

Amy is 10 year old

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