The sum of the ages of Dave and Ted is 48. Eight years from now, Ted will be 3x Dave's age. Find their present age.
d+t = 48
t+8 = 3(d+8)
Now just solve for d and t.
To solve this problem, we can set up a system of equations.
Let's assume Dave's present age is x and Ted's present age is y.
From the problem, we know two things:
1. The sum of the ages of Dave and Ted is 48.
This can be written as: x + y = 48
2. Eight years from now, Ted will be 3 times Dave's age.
This can be written as: (x + 8) = 3 * (y + 8)
We can simplify the second equation by expanding it:
x + 8 = 3y + 24
Now we have a system of two equations:
x + y = 48 (equation 1)
x + 8 = 3y + 24 (equation 2)
To solve this system, we can use the method of substitution.
From equation 1, we can express x in terms of y:
x = 48 - y
Now we substitute this value of x into equation 2:
48 - y + 8 = 3y + 24
Simplifying, we get:
56 - y = 3y + 24
Next, we move the terms involving y to one side and the constant terms to the other side:
56 - 24 = 3y + y
32 = 4y
Now, divide both sides of the equation by 4 to solve for y:
y = 32/4
y = 8
Substitute this value of y back into equation 1 to solve for x:
x + 8 = 3 * (8 + 8)
x + 8 = 3 * 16
x + 8 = 48
x = 48 - 8
x = 40
Therefore, Dave's present age (x) is 40, and Ted's present age (y) is 8.