A mother is three times as old as her daughter. Ten years ago, she was five times as old as her daughter. What are their present ages?
Question
A mother is three times as old as her daughter. Ten years ago, she was five times as old as her daughter. What are their present ages?
Solution
Let's denote the daughter's current age as D and the mother's current age as M.
From the problem, we have two equations:
-
M = 3D (The mother is three times as old as her daughter)
-
M - 10 = 5(D - 10) (Ten years ago, the mother was five times as old as her daughter)
Now, we can solve these equations step by step:
Step 1: Substitute M from equation 1) into equation 2):
3D - 10 = 5D - 50
Step 2: Rearrange the equation to isolate D:
50 - 10 = 5D - 3D
40 = 2D
Step 3: Solve for D:
D = 40 / 2 = 20
Step 4: Substitute D = 20 into equation 1) to find M:
M = 3 * 20 = 60
So, the daughter is 20 years old and the mother is 60 years old.
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