SOLUTION: Two years ago a woman was 7 times as old as her daughter but in three years, she will be four times as old as the girl. How old is the lady now?
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Question 1089455: Two years ago a woman was 7 times as old as her daughter but in three years, she will be four times as old as the girl. How old is the lady now? Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39618) (Show Source):
The correct system of equations is
M - 2 = 7*(D - 2), (1)
M + 3 = 4*(D + 3). (2)
Simplify this system:
M - 2 = 7D - 14 (1')
M + 3 = 4D + 12 (2')
M = 7D - 12, (1'')
M = 4D + 9, (2'')
====> 7D - 12 = 4D + 9 ====> 7D - 4D = 9 + 12 ====> 3D = 21 ===> D = 7.
Daughter is 7 years old now. The mother is (from (2'')) M = 4D + 9 = 4*7 + 9 = 28 + 9 = 37.
Answer. The mother is 37 years now.
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