Question 572991

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!