A man has a daughter and son. The son is three times older than the daughter. In one year the man will be six times as old as the daughter is now. In ten years the man will be fourteen year older than the combined ages of his children at that time. What is the mans present age?
s = 3d
m+1 = 6d
m+10 = 14+(s+10)+(d+10)
solve to find m.
I get non-integer values for s and d.
If "three times older" means d+3d=4d, then I get integer values, but the man is 149. Not likely.
To solve this problem, we need to set up equations based on the information given and then solve them simultaneously.
Let's define the present ages of the daughter, son, and the man as D, S, and M respectively.
According to the problem, the son is three times older than the daughter, so we can set up the equation: S = 3D.
In one year, the man will be six times as old as the daughter is now, so we have the equation: M + 1 = 6D.
In ten years, the man will be fourteen years older than the combined ages of his children at that time. We can express this as: M + 10 = 14 + (D + 10) + (S + 10).
Now we have a system of three equations with three variables. We can solve them to find the values of D, S, and M.
1. Substitute S = 3D into the equation M + 1 = 6D:
M + 1 = 6(3D)
M + 1 = 18D
2. Substitute S = 3D into the equation M + 10 = 14 + (D + 10) + (S + 10):
M + 10 = 14 + (D + 10) + (3D + 10)
M + 10 = 24 + 4D + 20
M + 10 = 4D + 44
3. Now we have two equations with two variables (M and D):
M + 1 = 18D --> Equation (1)
M + 10 = 4D + 44 --> Equation (2)
4. Solve the system of equations (1) and (2):
Subtract equation (1) from equation (2): (M + 10) - (M + 1) = (4D + 44) - (18D)
9 = -14D + 44
9 - 44 = -14D
-35 = -14D
To isolate D, divide both sides by -14, remembering to change the sign:
D = -35 / -14
D = 2.5
5. Now that we have the value of D, we can substitute it back into the equation S = 3D to find S:
S = 3(2.5)
S = 7.5
6. Finally, we can substitute the values of D and S into the equation M + 1 = 18D to find M:
M + 1 = 18(2.5)
M + 1 = 45
M = 45 - 1
M = 44
Therefore, the man's present age is 44 years old.