In 5 years time I will be 3 times as old as my son. In 14 years time, the sum of our ages will be 62. Today the sum of our ages is
Me: m
Son: s
You can answer the question without knowing either age:
In 14 years, I will be m+14, and son will be s+14
m+14 + s+14 = 62
m+s = 34
However, I think they wanted you to solve two simultaneous equations:
m+5 = 3(s+5)
m+14 + s+14 = 62
m=28, s=6
check: 28+5 = 33 = 3(6+5)
To find the sum of your ages today, we need to solve the given problem step by step.
Let's assume your current age is represented by "x," and your son's age is represented by "y."
From the first statement, "In 5 years time, I will be 3 times as old as my son," we can set up the equation:
x + 5 = 3(y + 5)
This equation states that in 5 years, your age (x + 5) will be three times your son's age (3(y + 5)).
Expanding the equation gives us:
x + 5 = 3y + 15
Next, let's consider the second statement, "In 14 years time, the sum of our ages will be 62." We can set up another equation:
(x + 14) + (y + 14) = 62
This equation represents the sum of your ages (x + 14) and your son's ages (y + 14) in 14 years, which will be equal to 62.
Now that we have two equations, we can solve the system of equations to find the values of x and y, representing your current ages and your son's current age.
Simplifying the equations:
Equation 1: x + 5 = 3y + 15
- x - 3y = 10
Equation 2: x + 14 + y + 14 = 62
x + y = 34
Now, we can solve the system of equations either by substitution or elimination.
Using the elimination method, we multiply Equation 1 by 2 to eliminate the x term:
-2x - 6y = 20
x + y = 34
Adding the two equations:
-2x - 6y + x + y = 20 + 34
- x - 5y = 54
Simplifying further, we have:
x + 5y = -54
Now we have:
-x - 5y = 54
x + 5y = -54
Adding the two equations:
0 = 0
Since 0 = 0, this means that the equations are dependent, and the variables can take on any value. This indicates that there are infinitely many solutions to this system of equations.
So, without additional information, we cannot determine the exact sum of your ages today.