Ten years ago the age of the father was four times of his son. Ten years hence the age of the father will be twice that of his son. The present ages of father & son are?
Does "hence" mean from "10 years ago"?
F = 2S
F-10 = 4(S-10)
Substitute 2S for F in the second equation and solve for S. Insert that value into the first equation to solve for F. Check by putting both values into the second equation.
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To solve this problem, we can use algebra to set up and solve a system of equations based on the given information.
Let's represent the present age of the son as "x" and the present age of the father as "y".
According to the given information, ten years ago, the age of the father was four times that of his son. This can be written as:
y - 10 = 4(x - 10)
Similarly, ten years hence (in the future), the age of the father will be twice that of his son. This can be written as:
y + 10 = 2(x + 10)
We now have a system of two equations:
y - 10 = 4(x - 10) ---- (Equation 1)
y + 10 = 2(x + 10) ---- (Equation 2)
To solve the system, we can substitute Equation 2 into Equation 1:
2(x + 10) - 10 = 4(x - 10)
Simplifying, we get:
2x + 20 - 10 = 4x - 40
2x + 10 = 4x - 40
40 + 10 = 4x - 2x
50 = 2x
x = 25
Now, substituting the value of x back into Equation 2 to find y:
y + 10 = 2(25 + 10)
y + 10 = 2(35)
y + 10 = 70
y = 70 - 10
y = 60
Therefore, the present age of the son is 25, and the present age of the father is 60.