A boy is 42 years younger than his father .In 8 years' times , he will be 1/4 times as old as his father .Find their present ages.
now:
father ---- x
son ------ x - 42
in 8 years:
father = x+8
son = x-42 + 8 = x - 34
x - 34 = (1/4)(x + 8)
x - 34 = x/4 + 2
each term times 4
4x - 136 = x + 8
3x = 144
x = 48
The father is now 48 and the son is now 6
check:
in 8 years, dad will be 56
son will be 14, and 14 is 1/4 of 56
All is good!
Let's represent the boy's age as x and the father's age as y.
According to the given information, the boy is 42 years younger than his father, so we have the equation:
x = y - 42
In 8 years' time, the boy's age will be x + 8, and the father's age will be y + 8. It is also stated that the boy will be 1/4 times as old as his father, so another equation can be made:
x + 8 = 1/4(y + 8)
Now we have a system of two equations with two variables. We can solve this system to find the present ages.
Substituting the value of x from the first equation into the second equation:
(y - 42) + 8 = 1/4(y + 8)
Simplifying the equation:
y - 34 = 1/4y + 2
Multiply both sides of the equation by 4 to remove the fraction:
4(y - 34) = y + 8
Expanding and simplifying the equation:
4y - 136 = y + 8
Subtracting y from both sides:
3y - 136 = 8
Adding 136 to both sides:
3y = 144
Dividing both sides by 3:
y = 48
Now we can substitute the value of y back into the first equation to find x:
x = y - 42
x = 48 - 42
x = 6
Therefore, the present age of the boy is 6 years and the present age of the father is 48 years.
To solve this problem, let's assign variables to the ages of the boy and his father.
Let x represent the boy's current age.
Then, the father's current age would be x + 42, since the boy is 42 years younger than his father.
In 8 years' time, the boy's age will be x + 8, and the father's age will be (x + 42) + 8 = x + 50.
According to the problem, the boy's age in 8 years will be 1/4 times the father's age in 8 years. We can represent this statement mathematically as:
(x + 8) = 1/4 * (x + 50)
To solve for x, we can multiply both sides of the equation by 4 to eliminate the fraction:
4 * (x + 8) = x + 50
Distribute the 4 on the left side:
4x + 32 = x + 50
Next, we can simplify the equation by subtracting x from both sides:
3x + 32 = 50
Subtract 32 from both sides:
3x = 18
Finally, divide both sides by 3:
x = 6
So, the boy's current age is 6 years old.
The father's current age is x + 42 = 6 + 42 = 48 years old.