Before 5 years a man was 3 years times his boy but after 10 years the father's age will be 6 more than 2 times his boy
I think your question is
"Five years ago a man was 3 times his boy's age. Ten years from now the father's age will by 6 more than 2 times his boy's age."
5 years ago:
son's age ---- x
father's age --- 3x
now:
son ---- x+5
father ---- 3x+5
10 years from now:
son = x+5 + 10 = x + 15
father = 3x+5 + 10 = 3x + 15
3x+15 = 2(x+15) + 6
3x + 15 = 2x + 36
solve for x and answer whatever your question is
To solve this problem, let's break it down step by step:
Let's assume the age of the boy presently is B and the age of the man (father) is M.
1. "Before 5 years, a man was 3 years times his boy."
This statement means that five years ago, the man's age was three times that of the boy's age.
So, we can write the equation: M - 5 = 3(B - 5).
2. "After 10 years, the father's age will be 6 more than 2 times his boy."
This statement means that ten years from now, the man's age will be six more than twice the boy's age.
So, we can write the equation: M + 10 = 2(B + 10) + 6.
Now, we have two equations with two variables (M and B). We can solve this system of equations to find the values of M and B.
From Equation 1: M - 5 = 3B - 15
Rearranging this equation: M = 3B - 10
Substituting the above value of M in Equation 2: (3B - 10) + 10 = 2(B + 10) + 6
Simplifying the equation: 3B - 10 + 10 = 2B + 20 + 6
Further simplifying: 3B = 2B + 26
Subtracting 2B from both sides: B = 26
Now, we know that the boy's age presently is 26.
To find the father's age, substitute the value of B in Equation 1: M = 3(26) - 10
Simplifying: M = 78 - 10
M = 68
Therefore, presently the boy is 26 years old, and the man (father) is 68 years old.