A man is four times as old as his daughter. Six years ago he was ten times as old as his daughter. How old are they now?
Daughter's age now = x
Man's age now = 4x
Six years ago, she was x-6 and he was 6x-6
4x-6 = 10(x-6)
easy to solve for x
To solve this problem, we can set up a system of equations.
Let's assume the daughter's age is x and the man's age is y.
According to the problem, "A man is four times as old as his daughter," we can write the equation:
y = 4x
Also, "Six years ago, he was ten times as old as his daughter," can be represented as:
y - 6 = 10(x - 6)
Now let's solve the system of equations:
Substitute the value of y in the second equation with 4x (from the first equation):
4x - 6 = 10(x - 6)
Distribute and simplify the equation:
4x - 6 = 10x - 60
4x - 10x = -60 + 6
-6x = -54
Divide by -6 on both sides to solve for x:
x = -54 / -6
x = 9
Now, substitute the value of x (daughter's age) into the first equation to find the man's age:
y = 4(9)
y = 36
Therefore, the daughter is 9 years old and the man is 36 years old.
m = man´s present age
d = daughter´s present age
A man is four times as old as his daughter means:
m = 4 d
Six years ago he was m - 6 years old , daughter was d - 6 ears old
Six years ago he was ten times as old as his daughter means:
m - 6 = 10 ( d - 6 )
Replace m with 4 d in this equation
4 d - 6 = 10 ( d - 6 )
4 d - 6 = 10 d - 60
Subtract 4 d to both sides
- 6 = 6 d - 60
Add 60 to both sides
54 = 6 d
6 d = 54
Divide both sides by 6
d = 9
m = 4 d = 4 ∙ 9 = 36
Now he is 36 years old
Proof:
m / d = 36 / 9 = 4
Six years ago he was 36 - 6 = 30 years old and
Six years ago daughter was 9 - 6 = 3 years old
30 / 3 = 10
Well, it sounds like the man is quite the expert in time travel if he was able to be ten times as old as his daughter six years ago. But let's use some good old-fashioned math to solve this conundrum.
Let's assume the daughter's age is "x" years now. According to the first statement, the man is four times as old as his daughter, so his age would be 4x.
Now, let's consider the second statement, which says that six years ago, the man was ten times as old as his daughter. So, if we subtract 6 from both their ages, we get 4x - 6 for the man's age and x - 6 for the daughter's age.
According to the second statement, we can set up the equation: 4x - 6 = 10(x - 6). Now it's time to put on our math hats and solve it.
Expanding the equation, we have 4x - 6 = 10x - 60. Rearranging the terms gives us 6x = 54, which simplifies to x = 9.
So, the daughter is 9 years old now. And since the man is four times as old, he would be 4 * 9 = 36 years old.
Thus, the man is 36 years old, and his daughter is 9 years old. Just remember, it's always a good idea to double-check my calculations. Otherwise, we might end up in some wibbly-wobbly mathematical mess!
Let's solve this problem step-by-step.
Let's say the current age of the daughter is represented by "D", and the current age of the man is represented by "M".
According to the problem, "A man is four times as old as his daughter":
M = 4D
And, "Six years ago he was ten times as old as his daughter":
(M - 6) = 10(D - 6)
Now, we can solve these equations simultaneously to find the values of M and D.
Substituting the value of M from the first equation into the second equation, we get:
(4D - 6) = 10(D - 6)
Expanding the brackets:
4D - 6 = 10D - 60
Rearranging the equation:
10D - 4D = 60 - 6
6D = 54
Dividing both sides by 6:
D = 9
Now, substitute the value of D back into the first equation to find the man's age:
M = 4D = 4 * 9 = 36
Therefore, the daughter is currently 9 years old, and the man is currently 36 years old.