.
The solution using two variables and two equations
Let x be the Bon's age and let y be the Sonia's (his daughter's) age.
From one side, we have this equation
x - y = 25 (1) ("Sonia is 25 years younger than her father".)
From the other side, we have second equation
x + 10 = 2*(y+10) (2) (in 10 years . . . )
So, we have the system of equations (1) and (2) in two unknowns.
To solve it, express x = 25 + y from eq(1), and substitute it into equation (2). You will get
(25 + y) + 10 = 2*(y+10)
35 + y = 2y + 20
35 - 20 = 2y - y
15 = y.
Thus Sonia is 15 years old now.
Hence, the father is x = 25 + y = 25 + 15 = 40 years old.
Answer. Sonia is 15 years old; the father is 40 years old.
Solved.
The solution using one variable and single equation
Let x be the Sonia's age.
Then the Bon's age is (x+25), according to the condition.
In 10 years Sonia's age will be (x+10) years, while Bon's age will be (x+25)+10 = (x+35).
Then the condition says
x + 35 = 2*(x+10).
It implies
x + 35 = 2x + 20
35 - 20 = 2x - x
15 = x.
And you get THE SAME ANSWER.
The second solution is completed.
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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
- Age problems for mental solution
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