Question 1146947: Three years ago.Rica was thrice as old as dandy.three years ago hence,she will be twice as old.Find their present age
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = age of rice today.
y = age of dandy today.
three years ago, rice was 3 times as old as dandy.
equation for that is:
x-3 = 3*(y-3)
today she is twice as old.
equation for that is x = 2*y
you have two equations that need to be solved simultaneously.
they are:
x = 2*y
x-3 = 3*(y-3)
simplify the second equation and leave the first equation as is to get:
x = 2y
x-3 = 3y-9
in the first equation, subtract 2y from both sides to get:
x - 2y = 0
in the second equation, subtract 3y from both sides and add 3 to both sides to get:
x - 3y = -6
your two equations are now:
x - 2y = 0
x - 3y = -6
subtract the second equation from the first to get:
y = 6
you were given that x = 2y, therefore x = 12
you have x = 12 and y = 6
you are given that x = 2y which becomes 12 = 2*6 which becomes 12 = 12 which is true.
you are given that x-3 = 3*(y-3) which becomes 12-3 = 3*(6-3) which becomes 9 = 3*3 which becomes 9 = 9 which is true.
both equations are true when x = 12 and y = 6
your solution is that rica is 12 years old and dandy is 6.
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