# Four years ago, Antonio is three times the age of his daughter Diana. In 10 years, he will be twice her age. How old are they now?

1
by Kasuminellie

2015-03-19T20:40:11+08:00

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This is what the statement means in mathematical form.

Let:       y = age of Diana
x = age of Antonio

x - 4 = 3 (y-4)
x + 10 = 2 (y + 10)

x -4    = 3y - 12
-   x+10 = 2y + 20
0 -14 =   y  - 32

-14 = y - 32
-14 + 32 = y
18 = y

x + 10 = 2y + 20
x        = 2y + 20 -10
x        = 2y + 10
x         = 2(18) + 10
x         = 36 + 10
x         = 46

Antonio's present age is 46 years old.
Diana's present age is 18 years old.

Check:
4 years ago, Antonio's age is 3 times the age of Diana.
46 - 4 = 18 - 4
42      = 14

42 is 3 times 14, Correct.

In 10 years, Antonio's age will be twice the age of Diana.
46 + 10 = 18 + 10
56 = 28
56 is twice of 28, Correct.