Question 91663: A mother is 30 years older than her daughter. Five years ago she was four times as old as her daughter. How old are they now?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Start by assigning variables to the unknown quantities:
Let M = Mother's present age.
Let D = Daughter's present age.
From the problem description we can write:
Mother's age is (M) is (=) 30 years older than her daughter's age, so:
M = D+30
Five years ago, Mother's age (M-5) was (=) four times her daughter's age, so
M-5 = 4(D-5) Simplify.
M-5 = 4D-20 Rewrite this as: (add 5 to both sides)
M = 4D-15 now substitute this for the M in the first equation.
D+30 = 4D-15 Simplify and solve for D by adding 15 to both sides.
D+45 = 4D Now subtract D from both sides.
45 = 3D Finally, divide both sides by 3.
15 = D or D = 15 This is the daughter's present age.
M = D+30
M = 15+30
M = 45 This is the mother's present age.
Check:
M = D+30
M = 15+30
M = 45
Five years ago:
M-5 = 4(D-5)
45-5 = 4(15-5)
40 = 4(10)
40 = 40
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