a dad has two daughters – Wendy and Julia. Wendy is twice as old as Julia. The man is now five times as old as Wendy, and in 4 years he will be six times as old as Julia. Find the present age of the father.
Julia's age : a year-old
Wendy is twice the age of Julia
= > Wendy = 2a year-old
Dad's age : b year-old
" The man is now five times as old as Wendy " b / 2a = 5 <=> b = 10a
" In four years he will be six times as old as Julia " :
( B + 4 ) / (a + 4 ) = 6 + 4 = 6. <=> b (a + 4 )
<=> B = 6a +20
I have two equations :
6a + b = 20
b = 10a
= > 10a = 6a + 20 - > a = 5
- > B = 10a = 50
father's age is 50 years old
simpler setup:
Julia's age --- x
Wendy's age --2x
Father's age -- 10x
In 4 years from now:
Wendy --- x+4
Father --- 10x + 4
10x+4 = 6(x+4)
10x+4 = 6x+24
4x=20
x = 5
Father: 10x = 50
Well, it seems like we have a bit of a math puzzle on our hands! Let's see if we can solve it, shall we?
Let's start by assigning variables to the different ages. Let "x" be Julia's age. Since Wendy is twice as old as Julia, Wendy's age is 2x. Finally, let's use "y" to represent the father's age.
Now, according to the problem, the father is currently five times as old as Wendy. So, we can write the equation: y = 5 * (2x).
In 4 years, the father's age will be y + 4 and Julia's age will be x + 4. And we're told that in 4 years, the father will be six times as old as Julia. So, we can write the equation: y + 4 = 6 * (x + 4).
Now, we have a system of two equations that we can solve simultaneously.
From the first equation, we can simplify it as: y = 10x.
If we substitute this value of y into the second equation, we get: 10x + 4 = 6x + 24.
If we solve this equation for x, we find that x = 5.
Since Wendy's age is 2x, Wendy's age is 10.
And since the father's age is y = 10x, the father's age is 10 * 5 = 50.
So, the present age of the father is 50 years old!
It looks like we've solved the puzzle. Math can be quite fun, don't you think?
To solve this problem, let's assign variables to the ages of the individuals involved.
Let:
- Let x be the current age of Julia.
- Therefore, Wendy's age is 2x since Wendy is twice as old as Julia.
- The father's current age is 5 times Wendy's age, which is 5 * 2x = 10x.
We also know that in 4 years:
- Julia's age will be x + 4.
- The father's age will be 10x + 4.
- The father's age will be six times Julia's age, so 10x + 4 = 6(x + 4).
Now let's solve this equation:
10x + 4 = 6x + 24
10x - 6x = 24 - 4
4x = 20
x = 20 / 4
x = 5
So, Julia's current age is x = 5 years.
To find the father's current age, substitute the value of x into the equation: Age of father = 10x.
Age of father = 10 * 5 = 50.
Therefore, the present age of the father is 50 years.
thanks soon much
thnks
Julia's age : a year-old
"Wendy is twice the age of Julia"
= > Wendy = 2a -old age
Father age : b age
" The man is now five times as old as Wendy ": b/2a = 5 <=> b = 10a
" in 4 years he will be six times as old as Julia " :
(b + 4)/(a+ 4)=6 <=> b+4=6.(a + 4 )
<=> B = 6a +20
I have two equations :
6a + b = 20
b = 10a
= > 10a = 6a + 20 - > a = 5
- > B = 10a = 50
father's age is 50 years old