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?

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): You can put this solution on YOUR website!
x, Mother
d, Daughter

Description is transcribed into this system:

~~(The solution for the system is not whole numbers.)~~

(mistake when first interpreted problem description)
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

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.

Solved.

There is a bunch of lessons on age word problems
    - Age problems and their solutions
    - A fresh formulation of a traditional age problem
    - Really intricate age word problem
    - Selected age word problems from the archive
in this site.

Read them and become an expert in solving age problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Age word problems".

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The solution by @josgarithmetic is WRONG.

For your safety, simply ignore it.

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