Question 572991: A mother is 3 times as old as her daughter. Seven years ago, she was 5 times as old. How old are the mother and daughter now?
Answer by mathsmiles(68)   (Show Source):
You can put this solution on YOUR website!
Let's let M = mother's age now.
D = daughter's age now.
M = 3 x D
Seven years ago, mother was M-7 years old; daughter was D-7 years old
At that time, mother was 5 times daughter's age.
M-7 = 5(D-7)
Substituting from the previous equation for mother's age:
(3D)-7 = 5(D-7) Multiplying out to remove the parens:
3D - 7 = 5D - 35
Subtract 3D from both sides of the equation:
-7 = 2D -35
Add 35 to both sides of the equation:
28 = 2D
Divide both sides by 2
14 = D
Daughter is 14, mother is 3 times her age, so 14x3 = 42
Checking:
Seven years ago, daughter was 7, mother was 35. Mother was 5 times as old as daughter. Correct!
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