Answer:
Li Ting's father: 40 years
Li Ting: 10 years
Step-by-step explanation:
Let F stand for Li Ting's father's current age, and L for Li Ting's current age.
We are told that "In five years' time, Li Ting's father will be three times as old as Li Ting" We can write that as:
(F+5) = 3*(L+5)
We are also told that "Four years ago, her father was six times as old as her." We can write that as:
(F-4) = 6(L-4)
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We have two equations and two unknowns. Find a way to eliminate one of the two variables (F or L) and solve for the remaining one.
(F+5) = 3*(L+5)
(F-4) = 6(L-4)
I'll choose the second equation and rearrange it to isolate F:
F = 6(L-4) + 4
F = 6L - 20
Now use this definition of F in the first equation:
(F+5) = 3*(L+5)
[6L-20]+5 = 3*(L+5)
6L - 20 + 5 = 3L + 15
3L = 15 +20 -5
3L = 30
L = 10 years old
Use this to solve either equation for F:
F = 6L - 20
F = 6*(10) - 20
F = 40 years old
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In five years:
F = 45, and L = 15 [Li Ting's father will be three times as old as Li Ting]
Four years ago:
F = 36 and L = 6 [Four years ago, her father was six times as old as her]
