the ratio of father's age to his son age is 8:3. in 5 year's time the sum of their ages will be 54. how old are they
let their ages be 8x and 3x
in 5 years:
father's age = 8x+5
son's age is 3x+5
8x+5 + 3x+5 = 54
solve for x, plug into my definitions
8xplus 5 plus 3x plus 5 is equal to 54
11x plus 10 is equal to 54
11x is equal to 54-10
11x is equal to 44
Divide by 11 both side
X is equal to 4
Let's say the father's age is represented by 8x and the son's age is represented by 3x, where x is a constant.
In 5 years, the father's age will be (8x + 5) and the son's age will be (3x + 5).
According to the given information, the sum of their ages in 5 years will be 54.
Therefore, we can write the equation:
(8x + 5) + (3x + 5) = 54
Simplifying the equation:
8x + 3x + 10 = 54
11x + 10 = 54
Now, let's solve for x:
11x = 54 - 10
11x = 44
Dividing both sides by 11:
x = 44 / 11
x = 4
Now that we have the value of x, we can find their ages.
The father's age = 8x = 8 * 4 = 32 years old.
The son's age = 3x = 3 * 4 = 12 years old.
Therefore, the father is 32 years old and the son is 12 years old.
To determine the father and son's current ages, we can set up a system of equations based on the given information.
Let's assume the father's current age is represented by "8x," and the son's current age is represented by "3x," where "x" is a constant.
According to the information given, in 5 years, the sum of their ages will be 54. Therefore, 5 years from now, the father's age will be 8x + 5, and the son's age will be 3x + 5.
So, we can write the equation:
(8x + 5) + (3x + 5) = 54
Simplifying the equation:
8x + 5 + 3x + 5 = 54
11x + 10 = 54
11x = 54 - 10
11x = 44
x = 44 / 11
x = 4
To find the ages of the father and son, we substitute the value of "x" back into our original assumption.
The father's current age is 8x, so 8 * 4 = 32.
The son's current age is 3x, so 3 * 4 = 12.
Therefore, the father is currently 32 years old, and the son is currently 12 years old.