# In 2 years a boy will be three fourths as old as his sister. two years ago he was two thirds as old as she. how old are they?

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by lewej

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by lewej

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3/4(x+2) - 2 = boy's age now

x-2 = sister's age 2 years ago

x+2 = sister's age in 2 years

2/3(x-2) = boy's age 2 years ago

3/4(x+2) = boy's age in 2 years

Since 4 years will be elapsed between 2 years ago and 2 years from now,

(3x+6)/4 - (2x-4)/3 = 4

(3(3x+6) - 4(2x-4))/12 = 4

(9x+18-8x+16)/12 = 4

x+34 = 48

x=48-34

x=14

=(3/4(x+2)) - 2

=(3/4(14+2) -2

=(48/4) - 2

=12-2

=10

The boy is 10 years old and the girl is 14 years old