Debbie’s age is 40% of her father’s age. Ten years ago from now, Debbie’s age will be 50% of her father’s age. How old are Debbie and her father now?
If the father's age is f, then
.40f + 10 = .50(f+10)
Father = 50
Debbie = 20
To find the ages of Debbie and her father, let's start by assigning variables to represent their ages.
Let D be Debbie's age and F be her father's age.
According to the problem, "Debbie’s age is 40% of her father’s age." can be written as D = 0.4F.
"Ten years ago from now, Debbie’s age will be 50% of her father’s age." can be written as D - 10 = 0.5(F - 10).
Now we have two equations:
Equation 1: D = 0.4F
Equation 2: D - 10 = 0.5(F - 10)
To solve the equations, we can substitute Equation 1 into Equation 2:
0.4F - 10 = 0.5(F - 10)
Now, let's simplify and solve for F:
0.4F - 10 = 0.5F - 5
0.5F - 0.4F = -5 + 10
0.1F = 5
F = 5 / 0.1
F = 50
Now, substitute the value of F back into Equation 1 to find Debbie's age:
D = 0.4F
D = 0.4 * 50
D = 20
Therefore, Debbie's age now is 20 and her father's age is 50.