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The sum of the ages of Dorothy and Dorileen is 41.In 5 years Dorothy will be twice as old as Dorileen.Find their ages 3 years ago.(Algebraic expressions and equations)

Sagot :

x + y = 41
y = 41-x

Present Ages:
Dorothy's age: x
Dorileen's age: 41-x

Ages in 5 years (add 5):  
Dorothy:  x + 5
Dorileen:  41 - x + 5  = (41+5) - x = 46 - x

Equation:  In five years, Dorothy will be twice as old as Dorileen
x + 5 = 2(46 - x)
x + 5 = 92 - 2x
2x + x = 92 - 5
3x = 87
3x/3 = 87/3
x = 29

Substitute x with 29:
Present ages:
Dorothy: x = 29 years old
Dorileen:  41 - x   ⇒   41 - 29 = 12 years old

FINAL ANSWER:
Ages 3 years ago (less 3):
Dorothy: 29-3 = 26 years old
Dorileen:  12 - 3 = 9 years old.